Question

prove :(sin theta + cos theta)(tan theta + cot theta)=sec theta + cosec theta

Answer 1

(Sin theta+ cos theta)(tan theta+cot theta)
(Sin theta+ cos theta)(sin/cos+cos/sin)
(Sin theta + cos theta)(1/sincos)
Sin theta + cos theta/sin cos
Sin/ sin cos+ cos/ sin cos
1/ cos+ 1/ sin
Sec theta + codec theta

Answer 2

(sin theta + cos theta ) (sin theta/cos theta + cos theta / sin theta)

(sin theta + cos theta ) ( sin² theta + cos² theta)
                                     ___________________  (LCM of sin theta, cos theta)
                                       sin theta cos theta
  
(sin theta + cos theta) (1)/sin theta cos theta

 [sin theta/sin theta cos theta + cos theta/sin theta cos theta]

sec theta + cosec theta 


Hope this helps you.