Question

Given that a+b = 90°, then find the value of
$\sqrt{cos \: a \: cosec \: b \: - \: cos \: a \: sin \: b}$
a) sin a
b) cos a
c) tan a
d) cot a

#ALIGARH MUSLIM UNIVERSITY ENTRANCE EXAMINATION

Answer 1

HELLO DEAR,

given that:-

a+b = 90°

a=(90-b)

or

b = (90° - a)

use this in the Equation
$\\ \\ \sqrt{cos(90 - b)cosecb - cos(90 - b)sinb} \\ \\ = > \sqrt{sinb \times \frac{1}{sinb} - sinb \times {sinb} } \\ \\ = > \sqrt{1 - {sin}^{2} b} = \sqrt{ {cos}^{2} b} = cosb \\ \\ = > cos(90 - a) = sina$


--------------or----------------

√[(cos a×cosec(90-a) - cosa×sin(90-a)]

=> √[cosa×1/cosa - cos ²a]

=> √(1-cos²a)

=> √(sin²a)

= sina

hence, option (a) is correct

I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

options a) is a correct answer.....