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If `alpha` and `beta` are the two different roots of equations `a cos theta+b sin theta=c`, prove that
(a) `tan (alpha+beta)=(2ab)/(a^(2)-b^(2))` (b) `cos(alpha+beta)=(a^(2)-b^(2))/(a^(2)+b^(2))`

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To prove the given statements, we start with the equation: \[ a \cos \theta + b \sin \theta = c \] ### Step 1: Rearranging the equation We can rearrange the equation to isolate \( b \sin \theta \): \[ b \sin \theta = c - a \cos \theta \] ...
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CENGAGE ENGLISH-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Concept App. 3.4
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  9. In a triangle ABC, if sin A sin(B-C)=sinC sin(A-B), then prove that co...

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

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

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

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

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

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

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  19. If cos theta= (cos alpha-cos beta)/(1- cos alpha cos beta), then prove...

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