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Implicit Differentiation

Prove that si...

Question

Prove that (sinA+cosecA)²+(cosA+secA)²=7+tan²A+cot²A

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Solution

=(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

Identities used:
1+tan²A=sec²A

1+cot²A=cosec²A

sin²A+cos²A=1

cosecA=1/sinA

secA=1/cosA

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Similar questions

Q. Prove that :

(sin A + c o s e c A)^{2} + (cos A + sec A)^{2} = 7 + {tan}^{2} A + {cot}^{2} A .

Q. Solve that:-

{(sin A + cos e c A)}^{2} + {(cos A + sec A)}^{2} = 7 + {tan}^{2} A + {cot}^{2} A

{(sin A + cos e c A)}^{2} + {(cos A + sec A)}^{2} = {tan}^{2} A + {cot}^{2} A + 7

(cos A + sec A)^{2} + {(sin A + cosec A)}^{2} - {tan}^{2} A - {cot}^{2} A .

Q. Prove that :

(s i n A + c o s e c A)^{2} + (c o s A + s e c A)^{2} = 7 + t a n^{2} A + c o t^{2} A .

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