Question

For acute angle θ; sec² θ = 1 − tan² θ.

Assertion (A): sec² θ = 1 − tan² θ is not a trigonometric identity.

Reason (R): For an acute angle θ, the trigonometric equation is an identity, if it is satisfied for every value of angle θ.

Options

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A.

Answer 1

Both A and R are true and R is the correct reason for A.

Explanation:

The valid trigonometric identity;

sec²θ = 1 + tan²θ

So, assertion (A) is true.

A trigonometric identity is an equation that holds true for all values of the variable (in this case, the angle θ) within its domain.

So, reason (R) is true.

∴ Both A and R are true and R is correct reason for A.