Question

prove that √1+sin a/√ 1-sin a + √1-sin a/√1+sin a = 2sec a

Answer 1

Step-by-step explanation:

√(1+ sin a)/√(1- sin a) +√(1-sin a)/√(1+sin a)=2sec a

LHS = √(1+ sin a)/√(1- sin x+a) +√(1-sin a) /√(1+sin a)

= √(1+ sin a)√(1- sin a)/(1- sin a) +√(1-sin a) √(1+sin a)/(1+sin a)

= √(1+ sin a) √(1- sin a) [1/(1-sin a)+ 1/(1+sin a)

= √(1- sin^2 a)[{1+sin a+1-sin a}/(1-sin^2 a)

= √cos^2 a)[2/(1-sin^2 a)

= 2 cos a/cos^2 a

= 2/cos a

= 2 sec a = RHS.

Hope this will be useful to to.