Choose the correct alternative answer for the following questions.
1 + tan2θ = ?
(A) cot2θ (B) cosec2θ (C) sec2θ (D) tan2θ

Chapter 6 – Trigonometry – Text Book Solution

Problem set 6| Q 1.3| Page 138

Choose the correct alternative answer for the following questions.

1 + tan²θ = ?
(A) cot²θ (B) cosec²θ (C) sec²θ (D) tan²θ

Solution

The correct answer is (C) sec2θ.

Proof:

We know that:

tan2θ = sin2θ/cos2θ

Adding 1 to both sides, we get:

1 + tan2θ = 1 + sin2θ/cos2θ

Taking the common denominator, we get:

(1 * cos2θ + sin2θ)/cos2θ

Using the identity sin2θ + cos2θ = 1, we can simplify the numerator to:

cos2θ + sin2θ = 1

Substituting this back into the expression, we get:

(1 * cos2θ + sin2θ)/cos2θ = (1/1) / cos2θ

Recall that secθ = 1/cosθ, so we can write this as:

1/(cos2θ) = sec2θ

Therefore, 1 + tan2θ = sec2θ, and the correct answer is (C).

Chapter 6 – Trigonometry – Text Book Solution

Problem Set 6 |Q 1.3| P 138

Q.1.2


Q 1.3


Q.1.4

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