Question

5. Prove that (sin cosec A)'(cos A + sec A) = 7 -tan-Acor A​

Answer 1

Step-by-step explanation:

1+tan²A=sec²A

1+cot²A=cosec²A

sin²A+cos²A=1  

cosecA=

secA=

: (sin A + cosec A)^2 + (cos A + sec A)^2 = 7 + tan^2A + cot^2A  

:

=(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

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