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( * ) If a cos theta + b sin theta = c then (a sin theta – b cos theta) square =

( * )
If a cos theta + b sin theta = c then (a sin theta – b cos theta) square = 

Grade:11

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below

acos\theta + bsin\theta = c…........(1)
Let
asin\theta - bcos\theta = d…....(2)
(1) + (2)
a^{2}cos^{2}\theta + b^{2}sin^{2}\theta + a^{2}sin^{2}\theta + b^{2}cos^{2}\theta = c^{2} + d^{2}
a^{2}(cos^{2}\theta + sin^{2}\theta) + b^{2}(sin^{2}\theta + cos^{2}\theta) = c^{2} + d^{2}
a^{2} + b^{2} = c^{2} + d^{2}
d^{2} = a^{2} + b^{2} - c^{2}

dhananjay
19 Points
7 years ago
asin theta+ bcos theta= ca/csin T + b/c cos T=1a/c sin T+ b/c cos T= sin^2T+cos^2Ta/c sin T + b/c cos T = sinT.sinT+cosT.cosT compare then a/b=sinT and b/c= cosTnow(acosT-bsinT)^2= (a×b/c- b×a/c)^2=0

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