Question

Write the value of cosec² (90° − θ) − tan² θ.

Answer 1

Answer:

The value of cosec²(90° - θ) − tan² θ is  1.

Step-by-step explanation:

Given : cosec²(90° - θ) − tan² θ  

= {cosec(90° - θ)²} − tan² θ  

= sec θ² - tan² θ

[By using , cosec(90°- θ ) = sec θ ]

cosec²(90° - θ) − tan² θ  = 1

[By using an identity sec² θ  - tan² θ = 1]

Hence, the value of cosec²(90° - θ) − tan² θ is  1.

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

According to the Question:

⇒ cosec²(90° - θ) − tan² θ

⇒ [cosec(90° - θ)²] − tan² θ

⇒ sec θ² - tan² θ

Note: Using - [ cosec(90°- θ ) = sec θ ]

⇒ cosec²(90° - θ) − tan² θ = 1

Note: Using identity - [ sec² θ - tan² θ = 1 ]

⇒ cosec²(90° - θ) − tan² θ

⇒ 1 ______________[ANSWER]