Question

prove that :root of( 1+ sin∅/1 - sin ∅) + root of ( 1 -sin∅/ 1+ sin∅) = 2 sec ∅

Answer 1

Hii friend,

Question:- ✓ ( 1+Sin theta / 1 - sin theta + ✓ 1- Sin theta / 1 + sin theta = 2 Sec theta

Solution:- We have,

LHS = ✓ 1+Sin theta / 1-Sin theta + ✓1 - Sin theta/ 1 + Sin theta.

= ✓1+Sin theta / ✓ 1-Sin theta + ✓1-Sin theta/ ✓ 1+Sin theta.

= (1+Sin theta) + (1-sin theta) / ✓(1-Sin theta)(1+Sin theta) .

= 2/✓(1-Sin² theta)

= 2/✓Cos² theta. [ 1-Sin² theta= Cos theta]

= 2/Cos

= 2×1/Cos

= 2Sec. [ 1/ Cos theta = Sec theta].

RHS = 2 Sec theta.

Hence,


LHS = RHS = 2 Sec theta...... Proved.....



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