Question

What is the value of (1 + tan²θ) (1 − sin θ) (1 + sin θ)?

Answer 1

Answer:

The value of (1 + tan²θ) (1 − sin θ) (1 + sin θ) is 1.

Step-by-step explanation:

Given : (1 + tan²θ) (1 − sin θ) (1 + sin θ)

= (1 + tan²θ) [(1 − sin θ) (1 + sin θ)]

= (1 + tan²θ) (1 − sin² θ)  

[By using identity , (a + b) (a - b) = a² - b²]

= sec² θ (1 − sin² θ)  

[By using  an identity, 1 +  tan² θ = sec² θ]

= sec² θ (cos² θ)  

[By using the identity, (1 - sin²θ) = cos²θ]

= 1/cos²θ × cos²θ

[By using the identity, secθ = 1/ cosθ]

= 1

(1 + tan²θ) (1 − sin θ) (1 + sin θ) = 1

Hence, the value of (1 + tan²θ) (1 − sin θ) (1 + sin θ) is 1.

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

According to the Question:

Refer to the attachment for step-by-step-explanation with answer.

⇒(1 + tan²θ) (1 − sin θ) (1 + sin θ) = 1

Hence Proved! ___________[ANSWER]