Question

If sec 'x+sec'y=π/2,
then the value of cosec 'x + cosec 'y is
​

Answer 1

Answer:

π / 2

Step-by-step explanation:

Given----> Sec⁻¹ x + Sec⁻¹ y = π / 2

To find ----> Value of ( Cosec⁻¹ x + Cosec⁻¹ y )

Solution-----> We know that,

Sec⁻¹ p + Cosec⁻¹ p = π / 2

=> Sec⁻¹ p = π / 2 - Cosec⁻¹ p

Applying this formula , we get

=> Sec⁻¹ x = π / 2 - Cosec⁻¹ x

And ,

=> Sec⁻¹ y = π / 2 - Cosec⁻¹ y

Now , returning to original problem , we have,

Sec⁻¹ x + Sec⁻¹ y = π / 2

=> π/2 - Cosec⁻¹x + π/2 - Cosec⁻¹ y = π / 2

=> - Cosec⁻¹ x - Cosec⁻¹ y = - π / 2

Changing the sign of whole equation

=> Cosec⁻¹ x + Cosec⁻¹ y = π / 2

Additional information---->

1) Sin⁻¹ x + Cos⁻¹ x = π / 2

2) tan⁻¹x + Cot⁻¹x = π / 2

3) tan⁻¹ x + tan⁻¹ y = tan⁻¹ (x +y )/(1 - xy )

4) tan⁻¹x - tan⁻¹y = tan⁻¹ ( x - y )/( 1 + xy )

Answer 2

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