Question

Find the value of x : xcot A .tan(90+A)= tan(90+A) . Cot(180- A)+ xsec (90+A) . Cosec A

Answer 1

Answer:

cot² A

Step-by-step explanation:

These are trigonometric rules:

tan(90+A) = - cot A

cot(180-A) = - cot A

sec(90+A) = - cosec A

So, substituting these accordingly,

the expression becomes:

xcot A .(-cot A) = (-cot A). (-cot A) + x(-cosec A). cosec A

=> -x(cot A)² = (cot A)² - x(cosec A)²

Rearranging,

x(cosec A)² - x(cot A)² = (cot A)²

that is,

x{(cosec A)² - (cot A)²} = (cot A)²

We know that (cosec² x - cot² x = 1), trigonometric identity.

So, x { 1 } = (cot A)²

That is, x = cot² A

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