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(sin ^2 3A )/( sin ^2 A ) -( cos^2 3A )...

`(sin ^2 3A )/( sin ^2 A ) -( cos^2 3A )/(cos ^2 A )` is

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`(sin^(2)3A)/(sin^(2)A)-(cos^(2)3A)/(cos^(2)A)`
`=(sin^(2)3Acos^(2)A-cos^(2)3Asin^(2)A)/(sin^(2)A cos^(2)A)`
`=(sin^(2)3A(1-sin^(2)A)-cos^(2)3Asin^(2)A)/(sin^(2)A cos^(2)A)`
`=(sin^(2)3A-sin^(2)A(cos^(2)3A+sin^(2)3A))/(sin^(2)Acos^(2)A)`
`=(sin(3A+A)sin(3A-A))/(sin^(2)A cos^(2)A)`
`=(sin(3A+A)sin(3A-A))/(sin^(2)Acos^(2)A)` .
`((4 sin A cos A cos 2A)(2sin A cos A))/(sin^(2)A cos^(2)A)=8cos2A`.
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CENGAGE-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise 3.4
  1. Prove that cosecA-2 cot 2A cos A=2sinA.

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  2. Prove that cos^(3)thetasin3theta+sin^(3)theta cos 3theta=(3)/(4)sin 4 ...

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  3. (sin ^2 3A )/( sin ^2 A ) -( cos^2 3A )/(cos ^2 A ) is

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  4. Prove that (1+sec 2 theta)(1+sec 4 theta)(1+sec 8 theta)=(Tan 8theta)/...

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  5. If in an isosceles triangle with base 'a', vertical angle 20^@ and lat...

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  6. In DeltaABC, a = 3, b = 4 and c = 5, then value of sinA + sin2B + sin...

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  7. If cos A = 3/4 then sin ""(A) /(2 ) . Sin 5 (A)/(2) is

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  8. Find the value of (4cos^(2)9^(@)-1)(4cos^(2)27^(@)-1) (4cos^(2)81^(@...

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  9. If theta is an acute angle and sin((theta)/(2))=sqrt((x-1)/(2x)) ,then...

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  10. In a triangle ABC, if sin A sin(B-C)=sinC sin(A-B), then prove that co...

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  11. Let a=(pi)/(7), then (a) show that sin^(2)3a-sin^(2)a=sin2asin3a (...

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  12. Show that 1/(sin 10^@) - sqrt3/(cos 10^@) = 4

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  13. Prove that 2 sin^2 beta + 4 cos(alpha + beta) sin alpha sin beta + co...

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  14. If tan x=(a)/(b) and tan 2x=(b)/(a+b) find the smallest positive value...

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  15. tantheta+tan(6 0^0+theta)+tan(12 0^0+theta)=3tan3theta

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  16. If A=110^(@), then prove that (1+sqrt(1+tan^(2)2A))/(tan2A)=-tan A.

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  17. If alpha and beta are the two different roots of equations alpha cos t...

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  18. If tan beta=cos theta tan alpha, then prove that tan^(2)""(theta)/(2)=...

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  19. If cos theta=a/(b+c), cos phi= b/(a+c) and cos psi=c/(a+b) where theta...

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  20. If cos theta=(cos alpha-cos beta)/(1-cos alpha cos beta),prove that ta...

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