Question

prove that : tan 15 degree + cot 15 degree = 4

Answer 1

Hi ,

LHS = tan 15 + cot 15

= ( 1 / cot 15 ) + ( cot 15 / 1 ) [ since tan A = 1 / cot A ]

= ( 1 + cot ^2 15 ) / ( cot 15 )

= ( cosec^2 15 ) / ( cot 15 )

[ since 1 + cot^2 A = cosec^2 A ]

= ( 1 / sin ^2 15 ) / ( cos 15 / sin 15 )

[ since cosec A = 1 / sin A , cot A = cos A / sin A ]

= 1 / ( sin 15 cos 15 )

Multiply numerator and denominator with 2

= 2 / ( 2sin15 cos 15 )

[ since 2sinA cosA = sin 2A ]

= 2 / sin 30

( since sin 30 = 1/2 )

= 2 / ( 1/2 )

= 2 × ( 2 /1 )

= 4

= RHS

I hope this helps you.

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