Question

Guys... Urgent plz Q.18????

Answer 1

Solution

A+B=90°

now..

$L.H.S. = \sqrt{ \cos(A) cosec(B) - \cos(A) \sin(B) } \\ = \sqrt{ \sin(90 - A) \cosec(B) - \cos(A)cos(90 - B) } \\ = \sqrt{ \sin(B) cosec(B) - \cos(A) \cos(A) } \\ = \sqrt{1 - \cos {}^{2} (A) } \\ = \sqrt{ \sin {}^{2} (A) } \\ = \sin(A) = R.H.S.(proved)$

Hope this helps you.....

Answer 2

Step-by-step explanation:

A + B = 90°.

We can write the same equation as,

B = 90 - A

Proof:

√cosAcosecB - cosAsinB

=> √cosAcosec(90 - A) - cosAsin(90 - A)

=> √cosAsecA - cosAcosA

[∴ secA = 1/cosA]

=> √cosA * 1/cosA - cos²A

=> √1 - cos²A

=> √sin²A

=> sinA

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