Solve for x in the following equations.

Question

((1+sinx)/cosx)+(cosx/((1+sinx))

Answer 1

The given equation is =

Apply pythagoreen identity :

Cancel common terms.

Answer 2

Given equation is( (1 +sinx)/cosx) + (cosx/(1+sinx)

Take L.C.M  ((1+sinx)^2 + (cosx)^2)/cosx(1+sinx)

It is in the form of (a+b)^2 = a^2 + b^2 + 2ab

(1 + sinx + 2sinx+cosx^2)/cosx(1+sinx)

We have formula sin^2x + cos^2x =1

(1 + 1 +2sinx)/(cosx +cosxsinx)

(2 +2sinx)/cosx(1+sinx)

Take common factor 2 in numerator

2(1 + sinx)/cosx(1 + sinx)

Cancel (1 + sinx) in numerator and denominator

2/cosx = 2secx

The solution for x = arccos(2)