Question

(sin teta + sec teta)^ + (cos teta+ cosec teta )^ = (1 + sec x cosec)^

Answer 1

`(sin\theta+sec\theta)^2+(cos\theta+cosec\theta)^2=(1+sec\theta\ cosec\theta)^2\\\\L=sin^2\theta+2sin\theta\cdot(1)/(cos\thewta)+(1)/(cos^2\theta)+cos^2\theta+2cos\theta\cdot(1)/(sin\theta)+(1)/(sin^2\theta)\\\\=(sin^2\theta+cos^2\theta)+(2sin\theta)/(cos\theta)+(2cos\theta)/(sin\theta)+(1)/(cos^2\theta)+(1)/(sin^2\theta)`


`=1+(2sin^2\theta+2cos^2\theta)/(sin\theta\ cos\theta)+(sin^2\theta+cos^2\theta)/(sin^2\theta\ cos^2\theta)\\\\=1+(2(sin^2\theta+cos^2\theta))/(sin\theta\ cos\theta)+(1)/(sin^2\theta\ cos^2\theta)\\\\=1+(2)/(sin\theta\ cos\theta)+(1)/(sin^2\theta\ cos^2\theta)\\\\=1^2+2sec\theta\ cosec\theta+sec^2\theta\ cosec^2\theta\\\\=(1+sec\theta\ cosec\theta)^2=R`