Question

sin2 60°/1-cos2 60°+cosec2 60°/1+cot2 60°​

Answer 1

Given : sin² 60°/(1-cos² 60°)  +cosec² 60°/(1+cot² 60°​)

To Find : Value

Solution

sin² 60°/(1-cos² 60°)  +cosec² 60°/(1+cot² 60°​)

sin²x + Cos²x= 1

=> 1 - Cos²x = sin²x

cosec²x = 1+cot²x

( cot x = Cosx/sinx  Hence 1+cot²x = 1 +  Cos²x/sin²x  = (sin²x  + Cos²x )/sin²x

= 1/sin²x = Cosec²x)

Hence   sin² 60°/(1-cos² 60°)  +cosec² 60°/(1+cot² 60°​)

=sin² 60°/ sin² 60°  + cosec² 60° /cosec² 60°

= 1  + 1

= 2

sin² 60°/(1-cos² 60°)  +cosec² 60°/(1+cot² 60°​) = 2

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