Grade 11Trigonometry

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

laxman

11 Years agoGrade 11

2 Answers

Jitender Singh

11 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

9 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