Question

Math Analysis: Simplify each expression(cos x/1+sinx) + (1+sinx/cosx)

Answer 1

Take LCM.
You'll get in the numerator- cos^2 x + (1+sinx)^2
= 2 + 2sinx
= 2(1+sinx)
in the denominator we have- (1+sinx)(cosx)

so answer is 2/cosx or 2secx.

Answer 2

i dont get it...

Answer 3

wait...i'll draw and tell.

Answer 4

Now write (1+sinx)^2 as 1 + (sinx)^2 + 2sinx [ (a+b)^2 = a^2 + b^2 +2ab]

now since (cosx)^2 + (sinx)^2 =1

so we have in the numerator = 1 + 1 + 2sinx
= 2 + 2sinx
= 2(1 + sinx)

in the denominator we have (1+sinx) as well. So it gets cancelled out. We are left with 2/cosx whixh is equal to 2secx.