Question

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

Answer 1

☆heya your answer is here☆

For convenience in writing theta is being taken as 'A' here
taking LHS
WE KNOW THAT sec A = 1/ cos A  ;   cosec A = 1/ sin A
=> ( sin A + 1/cos A) 2 + ( cos A + 1/ sin A)2
=> (sin2A + 1/cos2A + 2sin A / cos A ) + ( cos2A + 1/ sin2A + 2cos A / sin A)
=>  sin2A + 1/cos2A + 2sin A / cos A  +  cos2A + 1/ sin2A + 2cos A / sin A
=> (sin2A + cos2A) +1/cos2A  + 1/ sin2A +2sin A / cosA+ 2cos A / sin A
=> 1 +  sec2A + cosec2A + 2(sinA / cosA  + cos A/ sin A)
=> 1 +  sec2A + cosec2A + 2((sin2A  + cos2A)/ (sin A cos A))
=> 1 +  sec2A + cosec2A + 2(1/ sin A cos A)
=> 1 +  sec2A + cosec2A + 2(sec A cosecA)
=> 1 + (sec A + cosecA)2Submit
  =  RHS

Answer 2

Answer: Drop a Thanks♥