Write the value of .

OR

If sin θ = cos θ, then find the value of 2tan θ + cos²θ

Given:

To find: the value of given expression

Explanation: given

But we know,

Substituting this in given expression, we get

On combining we get

But we know sin²θ + cos²θ = 1

⇒ sin²θ = 1 – cos²θ

Now substituting the above value in equation (i), we get

= – 1

Hence the given value of the expression is–1

OR

Given: sin θ = cos θ

To find: the value of 2 tan θ + cos²θ

Explanation: given sin θ = cos θ

But we know this equal to tan θ

Hence tan θ = 1

But this is possible for the value

θ = 45°………. (i)

We will take the next expression,

2 tan θ + cos²θ

Substituting the value of θ from equation (i), we get

2tan (45°) + cos²(45°) ………. (ii)

We know tan (45°) = 1 and cos (45°)

Substituting these values in equation (ii), we get

Hence the value of 2 tan θ + cos²θ =