P If tan find the value of p.cos 20 + q sin 20. 9
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We have, cos20−sin20=p ...(1)
Squaring equation (1) we get,
cos
2
20+sin
2
20−2sin20cos20=p
2
1+sin(2×20)=p
2
⇒sin40=1−p
2
{∵2sinθcosθ=sin2θ}
cos40=
1−sin
2
40
⇒cos40=
1−(1−p
2
)
2
=p
2−p
2
Ans: B
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