Trigonometric RatiosHard

Question

Exact value of tan 200o (cot 10o − tan 10o) is-

Options

A.1
B.2
C.0
D.None of these

Solution

tan(180 + 20 )(cos 10 /sin 10 - sin 10/cos 10)
Equating the equation :- tan(180 + 20 ) = tan 20  : 
tan 20 ( cos 210 - sin 210) / sin10.cos 10
⇒  cos 2θ - sin 2θ = cos 2θ
⇒  2sinθ.cos θ = sin 2 θ
∴ tan 20 (cos 20 / sin 20)
 = 1 ans

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