Question

Sin 50 +sin 40 =
$sin(50) + sin(40) = rut 2 \sin(85)$
​

Answer 1

Answer:

LHS =sin40∘cos50∘+cos40∘sin50∘

=sin40∘cos(90∘−40∘)+cos40∘sin(90∘−40∘)

=sin40∘+sin40∘+cos40∘cos40∘

=sin240∘+cos240∘=1=RHS. Hence proved

ii) LHS =cot(270∘−θ)cot(270∘+θ)cot(540∘−θ)

=tanθ(−tanθ).cot(360∘+(180∘−θ).cot(360∘+(180∘+θ))

−tan2θ.cot(180∘−θ).cot(180∘+θ)

−tan2θ(−cotθ)(cotθ)

−1cot2θ(−cot2θ)

=1=RHS Hence Proved.

iii) LHS=cosπ8+cos(3π)8+cos(5π)8+cos(7π)8

=cosπ8+cos(3π)8+cos(π−3π8)+cos(π−π8)

=cosπ8+cos(3π)8−cos(3π)8−cosπ8

=0 = RHS Hence proved

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Explanation: