Question

if tan theta + cot theta is equal to 2 find sin theta​

Answer 1

Answer

Value of sin theta is 1/√2

Step-by-step explanation:

Given=

tan theta + cot theta = 2

Let's assume that

tan theta = x

Cot theta = 1/X. ( because cot is reverse of tan )

So,

$x + \frac{1}{x} = 2$

Taking LCM

$\frac{ {x}^{2} + 1 }{x} = 2$

Now , cross multiple

${x}^{2} + 1 = 2x$

Taking all digits to LHS

x²-2x+1 = 0

The above equation can be written as

(x-1)² =0

And (x-1)² became equal to 0 when the value of x will 1

So, value of x is 1

Then , tan theta = 1

Value of tan at 45° is 1 . So,

tan 45 ° = 1

theta = 45°

Sin theta = sin 45°

Sin 45° = 1/√2

Hope it may help you