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(1+sin2A-cos2A)/(1+sin2A+cos2A)=tanA...

`(1+sin2A-cos2A)/(1+sin2A+cos2A)=tanA`

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`(1+sin 2A-cos^(2)A)/(1+sin2A+cos2A)=((1-cos2A)+sin2A)/((1+cos2A)+sin2A)`
`=(2sin^(2)A+2sinAcosA)/(2cos^(2)A+2sinA cos A)`
`=(2sin A(sinA+cosA))/(2cosA(sinA+cosA))=tanA`
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CENGAGE-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise 3.4
  1. (1+sin2A-cos2A)/(1+sin2A+cos2A)=tanA

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  2. Prove that (1+sin2A)/(cos2A)=(cosA+sinA)/(cosA-sinA)=tan((pi)/(4)+A)

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  3. Prove that cot theta-tan theta=2cot 2 theta.

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  4. Prove that (cos theta-sintheta)/(cos theta+sintheta)=sec 2 theta-tan 2...

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  5. tan(pi/4+theta)-tan(pi/4-theta)=2tan2theta

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  6. Prove that cosecA-2 cot 2A cos A=2sinA.

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

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

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

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

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

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  12. If cosA=3/4, then 32 sin, A/2 sin, (5A)/2= (A) sqrt(11) (B) -sqrt(11) ...

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

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

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

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

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

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

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

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

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