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Prove each of the following identities :...

Prove each of the following identities :
` (1+ cos theta - sin^(2) theta)/(sin theta (1+ cos theta)) = cot theta `

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Prove: (1+cos theta-sin^(2)theta)/(sin theta(1+cos theta))=cot theta

Show that ((1 + cos theta - sin ^(2) theta)/( sin theta (1 + cos theta ))) = cot theta

Prove each of the following identities : (cos^(3) theta + sin^(3) theta)/(cos theta + sin theta ) + (cos^(3) theta - sin^(3) theta)/(cos theta - sin theta ) = 2

Prove each of the following identities : (i) (1+ cos theta + sin theta)/(1+ cos theta - sin theta) =(1+ sin theta)/(cos theta) (ii) (sin theta + 1- cos theta)/(cos theta - 1 + sin theta) = (1+ sin theta)/(cos theta)

Prove each of the following identities : (i) (sin theta - cos theta)/(sin theta + cos theta) + ( sin theta+ cos theta)/(sin theta - cos theta) = (2)/((2 sin^(2) theta -1)) (ii) (sin theta + cos theta ) /(sin theta - cos theta) + ( sin theta - cos theta) /(sin theta + cos theta) = (2) /((1- 2 cos^(2) theta))

Prove each of the following identities : (sin theta + cos theta)/(sin theta - cos theta) + (sin theta - cos theta)/(sin theta + cos theta) = (2) /((sin^(2) theta - cos^(2) theta)) = (2) /((2sin^(2) theta -1))

Prove each of the following identities : (cos theta) /((1- tan theta)) - (sin^(2) theta)/((cos theta - sin theta)) = (cos theta + sin theta)

Prove each of the following identities : ( cos^(2) theta)/((1- tan theta)) + (sin^(3) theta)/((sin theta - cos theta)) = (1+ sin theta cos theta)

Prove each of the following identities : (1+ tan theta + cot theta )( sin theta - cos theta ) =((sec theta)/("cosec"^(2) theta ) - ("cosec"theta)/(sec^(2)theta))

Prove the following identities: (cos ec theta-sin theta)(sec theta-cos theta)=(1)/(tan theta+cot theta)

VK GLOBAL PUBLICATION-INTRODUCTION TO TRIGONOMETRY-SHORT ANSWER QUESTIONS-II
  1. If sectheta=x+1/(4x),p rov et h a t :sectheta+tantheta=2xor ,1/(2x)

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

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

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

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

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

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

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

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

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

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

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

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

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  14. Prove that: (sin theta - 2 sin^(3) theta) = (2cos^(3) theta - cos the...

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  15. (sin A+cosec A)^(2)+(cos A+sec A)^(2)=7+tan^(2)A+cot^(2)A

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  16. Prove each of the following identities : (1+ cos theta - sin^(2) th...

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  17. 1/(sinA+cosA+1)+1/(sinA+cosA-1)=secA+c o s e c A

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  18. Prove that (cos A)/(1+sin A)+(1+sin A)/(cos A)=2sec A

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  19. Evaluate : (sec^(2)theta-cot^(2)(90^(@)-theta))/("cosec"^(2)67^(@)-tan...

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  20. Evaluate : (sec theta ."cosec" (90^(@) - theta) - tan theta.cot (90^(@...

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