Question

(sin theta + sec theta)^2 + (cos theta + cosec theta )^2=(1+sec theta cosec theta)^2

Answer 1

LHS⇒sin²Ф+2sinФsecФ+sec²Ф+cos²Ф+2cosФcosecФ+cosec²Ф
        =sin²Ф+cos²Ф+1/cos²Ф+1/sin²Ф+2×sinФ×1/cosФ+2×cosФ×1/sinФ
        =1 + 1/sin²Фcos²Ф + 2sinФ/cosФ + 2cos/sinФ
        =1 + 1/sin²Фcos²Ф + 2(sin²Ф+cos²Ф)/sinФcosФ
        =1 + 1/sin²Ф × cos²Ф + 2(1/sinФ × 1/cosФ)
        =1 + cosec²Фsec²Ф + 2cosecФsecФ

RHS⇒1² + 2cosecФsecФ + cosec²Фsec²Ф

LHS = RHS
hence proved