Express sin A - A and tan A in terms of A-

Sin A = 1/cosec A = 1/√(cosec^2 A) = 1/√(1 + cot^2 A) sec A = 1/cos A = 1/sin A/cos A/sin A ............(Dividing num. and deno. be sin A ) ⇒ cosec ...

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Standard X

Mathematics

Trigonometric Identity- 1

Express sin A...

Question

Express sin A, sec A and tan A in terms of cot A.

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Solution

sin A = $\frac{1}{c o s e c A}$ = $\frac{1}{\sqrt{c o s e c^{2} A}}$ = $\frac{1}{\sqrt{1 + c o t^{2} A}}$

sec A = $\frac{1}{c o s A}$ = $\frac{\frac{1}{s i n A}}{\frac{c o s A}{s i n A}}$ ............(Dividing num. and deno. be sin A )

$\Rightarrow$ $\frac{c o s e c A}{c o t A}$ = $\frac{\sqrt{1 + c o t^{2} A}}{c o t A}$ and

tan A = $\frac{1}{c o t A}$

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Express sin A, sec A and tan A in terms of cot A.

sin A = 1cosecA = 1√cosec2A = 1√1+cot2A sec A = 1cosA = 1sinAcosAsinA ............(Dividing num. and deno. be sin A ) ⇒ cosecAcotA = √1+cot2AcotA and tan A = 1cotA