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Question
Prove that sin (90° - θ) cos (90° - θ) = tan θ. cos2θ.
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Solution
LHS = sin (90° - θ) cos (90° - θ)
LHS = cos θ. sin θ
RHS = tan θ. cos2θ
RHS = `sin θ/cos θ` x cos2θ
RHS = cos θ. sin θ
∴ LHS = RHS
Hence proved.
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sin4A – cos4A = 1 – 2cos2A. For proof of this complete the activity given below.
Activity:
L.H.S. = `square`
= (sin2A + cos2A) `(square)`
= `1 (square)` ...`[sin^2"A" + square = 1]`
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= `square`
= R.H.S.
Prove the following:
(sin α + cos α)(tan α + cot α) = sec α + cosec α
