Question

PLZ...help me out!

Prove this!!
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Answer 1

Answer:

Step-by-step explanation:

sinФ/(secФ+tanФ-1) + cosФ/(cosecФ+cotФ-1)

=sinФ/(1/cosФ+sinФ/cosФ-1) + cosФ/(1/sinФ+cosФ/sinФ-1)

=sinФ/{(1+sinФ-cosФ)/cosФ} + cosФ/{(1+cosФ-sinФ)/sinФ}

=sinФcosФ/(1+sinФ-cosФ) + sinФcosФ/(1+cosФ-sinФ)

=sinФcosФ[(1+cosФ-sinФ+1+sinФ-cosФ)/(1+sinФ-cosФ)(1+cosФ-sinФ)]

=2sinФcosФ/(1+sinФ-cosФ+cosФ+sinФcosФ-cos²Ф-sinФ-sin²Ф+sinФcosФ)

=2sinФcosФ/{1+2sinФcosФ-(sin²Ф+cos²Ф)}

=2sinФcosФ/(1+2sinФcosФ-1)

=2sinФcosФ/2sinФcosФ

=1

hence proved

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