Question

the value of 3 cosec square 38degree - 3 tan square 52

Answer 1

Answer:

here is your ans

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Answer 2

Answer:

3

Step-by-step explanation:

Given---> 3 Cosec² 38° - 3 tan² 38°

To find ---> Value of given expression

Solution---> We know that ,

Cosec ( 90° - θ ) = Secθ

Now , we have to find value of ,

3 Cosec² 38° - 3 tan²52°

= 3 Cosec² ( 90° - 52° ) - 3 tan² 52°

= 3 { Cosec ( 90° - 52° ) }² - 3 tan² 52°

Applying above formula, we get,

= 3 ( Sec 52° )² - 3 tan² 52°

= 3 Sec² 52° - 3 tan² 52°

= 3 ( Sec² 52° - tan² 52° )

We know that , Sec²θ - tan²θ = 1 , applying it here we get ,

= 3 ( 1 )

= 3

Additional identities--->

1) Sin( 90° - θ ) = Cosθ

2) Cos( 90° - θ ) = Sinθ

3) tan ( 90° - θ ) = Cotθ

4) Cot ( 90° - θ ) = tanθ

5) Sec ( 90° - θ ) = Cosecθ

6) Sin²θ + Cos²θ = 1

7) 1 + tan²θ = Sec²θ

8) 1 + Cot²θ = Cosec²θ

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