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Prove taht {(1-cot^2((alpha-pi)/4))/(1+c...

Prove taht `{(1-cot^2((alpha-pi)/4))/(1+cot^2((alpha-pi)/4))+cos(alpha/2)cot(4alpha)}sec((9alpha)/2)=cosec4alpha`

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Prove taht {(1-cot^(2)((alpha-pi)/(4)))/(1+cot^(2)((alpha-pi)/(4)))+cos((alpha)/(2))cot(4 alpha)}sec((9 alpha)/(2))=cos ec4 alpha

Prove that {(1-cot^(2)((a-pi)/(4)))/(1+cot^(2)((a-pi)/(4)))+cos((a)/(2))*cot4a}sec((9 pi)/(2))=cos ec4 alpha

Prove that: [1+cot alpha-sec((pi)/(2)+alpha)][1+cot alpha+sec((pi)/(2)+alpha)]=2cot alpha

Prove that: (tan^(3)alpha)/(1+tan^(2)alpha)+(cot^(3)alpha)/(1+cot^(2)alpha)=sec alpha cosec alpha-2sin alpha cos alpha

Show that 1+cot^2alpha/(1+cosecalpha)=cosec alpha

cot^(2)alpha=1+a^(2) then cos ec alpha+cot^(3)alpha sec alpha=

cot^(2)alpha=1+a^(2) then cos ec alpha+cot^(3)alpha sec alpha=

(1+cot alpha+cos ec alpha)/(1-cot alpha+cos ec alpha)

2sec^(2)alpha-sec^(4)alpha-2csc^(2)alpha+csc^(4)alpha=

(1+cot alpha+cos ec alpha)/(1-cot alpha+cos ec alpha)=

MOTION-TRIGNOMETRIC RATIOS & IDENTITIES -Exercise -3
  1. If A+B+C =180^(@) then prove that sin 2A + sin 2B+ sin 2C = 4 sin A s...

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  2. If tan x=(3)/(4) " and " pi lt x lt .(3pi)/(2) find the value of ...

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  3. Prove taht {(1-cot^2((alpha-pi)/4))/(1+cot^2((alpha-pi)/4))+cos(alpha/...

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  4. 4(cos^3 2 0^(@)+cos^3 4 0^(@))=3(cos2 0^(@)+cos4 0^(@))

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  5. Prove that (i) (sec 8A -1)/(sec 4A -1) =(tan 8A)/(tan 2A) (ii) (c...

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  6. Prove that sin 3x .sin^(3) x+cos 3 x . Cos^(3)x=cos^(3) 2x

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  7. If tan beta=(tan alpha + tan gamma)/(1+ tan alpha . tan gamma) Prove...

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  8. Prove that sin^2 theta+sin^2 2theta+sin^2 3theta+....+sin^2 n theta=n/...

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  9. सिद्ध कीजिए कि - cos x+cos ((2pi)/(3)+x)+cos((2pi)/(3)-x)=0

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  10. Find the maximum and minimum values of (i) cos 2x + cos^(2)x (ii) ...

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  11. An maximum value of 1+4 sin theta + 3 cos theta is

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  12. If phi is the exterior angle of a regular polygon of n sides and theta...

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  13. If - pi/2 < x < pi/2 and y=log10(tanxsecx). Then the expression E=(10^...

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  14. If the arcs of the same length in two circles subtend angles 75^(@) a...

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  15. Find the length of an arc of a circle of radius 10 cm which subtends ...

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  16. If cos(alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)=-3/2 , prove that ...

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  17. For all theta in [ 0, pi//2], show that cos ( sin theta) gt sin (cos...

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  18. Calculate the following without using trigonometric tables (i) tan ...

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  19. If sin(theta+alpha)=asin(theta+beta)=b(0 lt alpha,beta,theta lt pi/2)...

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  20. If A+B+C=pi prove that tan B tan C+tanc tan A+ tan A tan B =1 +sec A....

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