20. Prove the following identity, where angle A is an acute angle:(sin

1.	20. Prove the following identity, where angle A is an acute angle:(sin A + cosec A)? + (cos A + sec A) 7 + tan?A + cot?A
Answer» (sinA+cosecA)²+(cosA+secA)² =sin²A+cosec²A+2sinAcosecA+cos²A+sec²A+2cosAsecA =sin²A+cos²A+cosec²A+sec²A+2sinA×1/sinA+2cosA×1/cosA =1+cosec²A+sec²A+2+2 =5+(1+cot²A)+(1+tan²A) =7+tan²A+cot²A Like my answer if you find it useful!

20. Prove the following identity, where angle A is an acute angle:(sin A + cosec A)? + (cos A + sec A) 7 + tan?A + cot?A

Answer»

(sinA+cosecA)²+(cosA+secA)²

=sin²A+cosec²A+2sinAcosecA+cos²A+sec²A+2cosAsecA

=sin²A+cos²A+cosec²A+sec²A+2sinA×1/sinA+2cosA×1/cosA

=1+cosec²A+sec²A+2+2

=5+(1+cot²A)+(1+tan²A)

=7+tan²A+cot²A

Like my answer if you find it useful!