Question

(Sin theta + cosec theta) square + (cos theta + Sec theta) square = (7+ tan square theta + cot square theta)​

Answer 1

let consider theta as A

LHS:

(sinA+cosecA) ^2+(cosA+secA) ^2

sin^2A+2sinA×cosecA+cosec^2A+cos^2A+2cosA×secA+sec^2A

sin^2A+cos^2A+2×1+2×1+cosec^2A+sec^2A

1+2+2+ 1+ tan^2A+1+cot^2A

7+tan^2A+cot^2A

RHS..

Here are the formula which help you to solve this:

sin^2A+cos^2A=1

sin^2A×cosec^2A=1

cos^2A×sec^2A=1

cosec^2A=1+cot^2A

sec^2A=1+tan^2A

Thanks