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Prove that (cos theta-sintheta)/(cos the...

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

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`(cos theta-sin theta)/(cos theta+sin tehta)=(cos theta-sin thetacos theta-sin theta)/(cos theta+sin theta cos theta-sin theta)`
`=(1-sin 2theta)/(cos 2theta)`
`=sec 2theta-tan 2 theta`.
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CENGAGE-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise 3.4
  1. Prove that (1+sin2A)/(cos2A)=(cosA+sinA)/(cosA-sinA)=tan((pi)/(4)+A)

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

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

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  4. Prove that tan ((pi)/(4) + theta)- tan ((pi)/(4) - theta) = 2 tan 2 th...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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