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Without using trigonometric tables, evaluate each of the following: `(sec^2 54^0-cot^2 36^0)/(cos e c^2 57^0-tan^2 33^0)+2sin^2 38^0sec^2 52^0-sin^2 45^0`

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The correct Answer is:
`(5)/(2)`
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Without using trigonometric tables,evaluate each of the following: (sec^(2)54^(0)-cot^(2)36^(@))/(cos ec^(2)57^(0)-tan^(2)33^(0))+2sin^(2)38^(@)sec^(2)52^(0)-sin^(2)45^(@)

Without using trigonometric tables, evaluate each of the following: (cos^2 20^0+cos^2 70^0)/(sec^2 50^0-cot^2 40^0)+2cosec^2 58^0-2cot58^0tan32^0- 4tan13^0tan37^0tan45^0tan53^0tan77^0

Without using trigonometric tables, evaluate the following: (sec37^0)/(cos e c53^0)+2cot15^0cot25^0cot45^0cot75^0cot65^0(sin^2 18^0+sin^2 72^0)

Without using trigonometric tables, evaluate each of the following : (i) sin^2 65^@+sin^2 25^@ (ii) cos^2 17^@- sin^2 73^@ (iii) cosec ^2 67^@-tan^223^@ (iv) sec^2 36^@-cot ^2 54^@ .

Without using trigonometric tables, evaluate each of the following: (-tanthetacot(90^0-theta)+secthetacos e c(90^0-theta)+sin^2 35^0+sin^2 55^0)/(tan10^0tan20^0tan30^0tan70^0tan80^0)

Without using trigonometric tables,evaluate each of the following: (sec39^(0))/(cos ec51^(0))+(2)/(sqrt(3))tan17^(0)tan38^(@)tan60^(@)tan52^(@)tan73^(@)-3(sin^(2)31^(0)+sin^(2)59^(@))

Without using trigonometric tables,evaluate each of the following: (2)/(3)cos ec^(2)58^(@)-(2)/(3)cot58^(@)tan32^(@)-(5)/(3)tan13^(0)tan37^(0)tan45^(@)tan53^(@)tan77^(0)

Without using trigonometric tables,evaluate each of the following: (sin^(2)20^(@)+sin^(2)70^(@))/(cos^(2)20^(0)+cos^(2)70^(@))+(sin(90^(@)-theta)sin theta)/(tan theta)+(cos(90^(@)-theta)cos theta)/(cot theta)+cos(40^(0)+theta)-sin(50^(@)-theta)+(cos^(2)40^(0)+cos^(2)50^(@))/(sin^(2)40^(0)+sin^(2)50^(@))

Without using trigonometric table,evaluate the following: (cos ec^(2)(90-theta)-tan^(2)theta)/(4(cos^(2)48^(@)+cos^(2)42^(@)))-(2tan^(2)30^(@)sec^(2)52^(@)sin^(2)38^(@))/(cos ec^(2)70^(@)-tan^(2)20^(@))

Evaluate (sec^2""54^@-cot^2""36^@)/(cosec^2""57^@-tan^2""33^@)+2sin^2""38sec^2""52^@-sin^2""45^@+2/sqrt3tan17^@tan60^@tan73^@

VK GLOBAL PUBLICATION-INTRODUCTION TO TRIGONOMETRY-SHORT ANSWER QUESTIONS-II
  1. If sin theta+cos theta=sqrt3, then prove that tan theta+cot theta=1

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  2. Prove the following identities: (1-sintheta)/(1+sintheta)= (sectheta...

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  3. Without using trigonometric tables, evaluate each of the following: (...

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  4. (2sin68^(@))/(cos22^(@))-(2cot15^(@))/(5tan75^(@))-(3tan45^(@).tan20^(...

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  5. (sin^(2) 20^(@) + sin^(2) 70^(@))/(cos^(2) 20^(@) + cos^(2) 70^(@)) + ...

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  6. Evaluate: sin 25^(@) cos 65^(@) + cos 25^(@) sin 65^(@).

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  7. Without using tables, evaluate the following: 3 cos 68^(@) . "cosec"...

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  8. If sin 3 theta = cso ( theta - 6^(@)) where 3 theta and theta - 6^(@) ...

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  9. If sectheta=x+1/(4x),p rov et h a t :sectheta+tantheta=2xor ,1/(2x)

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  10. Find an acute angle theta , when (costheta-sintheta)/(costheta+sinthet...

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  11. The altitude A D of a A B C , in which /A obtuse and, A D=10c mdot If...

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  12. If cos e c\ theta=(13)/(12) , find the value of (2sintheta-3\ cos\ ...

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  13. Prove that (tan A )/(1 + sec A) - (tan A )/(1 - sec A ) = 2 cosec A.

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  14. Prove: (cos^(3)theta+sin^(3)theta)/(cos theta+sin theta)+(cos^(3)theta...

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  15. सिद्ध करें कि cot theta-tan theta=(2 cos^(2)theta-1)/(sin theta*cos...

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  16. Prove that (cot^(2)theta)/(cosec theta+1)=cosec theta-1

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  17. Evaluate the (sin 30^(@) + tan 45^(@) - "cosec" 60^(@))/(sec 30^(@)...

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  18. Evaluate the following (i) s in"\ "60o"\ "cos"\ "30o"\ "+"\ "s in"...

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  19. If tan(A+B)=sqrt(3) and t a n(A B)=1/(sqrt(3)); 0o<A+Blt=90o;""...

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  20. If A, B and C are interior angles of a triangle ABC, then show that si...

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