IPMAT/Algebra•9mos
bheem0001

TRIGNOMETRY DOUBT

how did sin(theta-alpha)*sin(theta+alpha) become sin(theta)^2-sin(alpha)^2???

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Comments (2)

D
dumboscupcake
IIM Sambalpur (BSMPP)
•9mos

(will be using @ as alpha and & as theta)

Sin(&-@)=sin&cos@-sin@cos& sin(&+@)=sin&cos@+sin@cos& (using the compound angle formulas)

Mulyiplying them we get sin^2&cos^@-sin^2@cos^2&

substituing cos^2@=1-sin^2@ and cos^2&=1-sin^2&

we get sin^2&(1-sin^2@)-sin^@(1-sin^2&)= sin^2&-sin^2&sin^2@-sin^2@+sin^2&sin^2@

the second term and the fourth term gets cancelled hence we get sin^2&-sin^2@

HENCE PROVED!

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B
bheem0001
OP•9mos

Silly me. Thank for your help

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