Question

Cos10+sin10/cos10-sin10

Answer 1

LHS = ( Cos 10 + Sin 10 ) / ( Cos 10 - Sin 10 )

{ Multiply numerator and and denominator with 1 / Cos 10 }

= [ 1 /Cos 10 ( Cos 10 + Sin 10 ) ] / [ 1/Cos 10 ( Cos 10 - Sin 10 ) ]

= [ Cos10 / Cos10 + Sin10 / Cos10 ] / [ Cos10 / Cos10 - Sin10 / Cos10 ]

= ( 1 + tan10 ) / ( 1 - tan 10 ) [ since sin 10 / cos 10 = tan 10 ]

= ( tan 45 + tan 10 ) / ( 1 - tan 45 tan 10 ) [ since tan 45 = 1 ]

= tan ( 45 + 10 )

[ since tan ( A + B ) = (tanA + tan B ) / (1 - tanAtanB)]

= tan 55

= tan ( 90 - 35 )

= cot 35 [ since tan ( 90 - A ) = cot A ]

= R H S

I hope this helps you

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