Question

(cosec-sin) (sec-cos) (tan+cot)=1

Answer 1

LHS:
=(cosecФsecФ-cosecФcosФ-sinФsecФ+sinФcosФ)(tanФ+cotФ)
=(1/sinФcosФ - cosФ/sinФ - sinФ/cosФ + sinФcosФ)(tanФ+cotФ)
=(1-cos²Ф-sin²Ф+(sinФcosФ)²)/sinФcosФ (tanФ+cotФ)
=(1-(cos²Ф+sin²Ф)+(sinФcosФ)²)/sinФcosФ (tanФ+cotФ)..as sin²Ф+cos²Ф=1
=(1-1+(sinФcosФ)²/sinФcosФ (tanФ+cotФ)
= (sinФcosФ)²/sinФcosФ (tanФ+cotФ)
= 1/1/sinФcosФ (tanФ+cotФ)...................as 1/1/sinФcosФ = sinФcosФ
= 1/sin²Ф+cos²Ф/sinФcosФ (tanФ+cotФ)
= 1/(sin²Ф/sinФcosФ + cos²Ф /sinФcosФ) (tanФ+cotФ)
=1/(sinФ/cosФ + cosФ/sinФ)  (tanФ+cotФ)
= 1/ (tanФ+cotФ)  (tanФ+cotФ)
= 1
Hence proved.

Answer 2

yes it is possible answer is 1