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question mark

Find the value of

Sin78 - Sin66 -Sin42 + Sin60

all angles are in degree.

Anurag Kshatri , 13 Years ago

Grade 12

1 Answers

Jitender Singh

Ans:Hello student, please find answer to your question
$V = sin(78)-sin(66)-sin(42)+sin(60)$
$V = sin(60+18)-sin(60-18)-sin(66)+sin(60)$
$sin(a+b) = sin(a).cos(b)+cos(a).sin(b)$
$sin(a-b) = sin(a).cos(b)-cos(a).sin(b)$
$V = sin(60).cos(18)+cos(60).sin(18)-(sin(60).cos(18)-cos(60).sin(18))-sin(66)+sin(60)$ $V = 2cos(60).sin(18)-sin(66)+sin(60)$
$V = 2.\frac{1}{2}.sin(18)-sin(66)+sin(60)$
$V = sin(18)-sin(66)+sin(60)$
$V = \frac{\sqrt{5}-1}{4}-cos(24)+\frac{\sqrt{3}}{2}$

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