Question #1850

Verify the identity
1+sinx/cosx+cosx/1+sinx=2secx

Expert's answer

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

Let's consider the left part of the expression:

((1+sinx)^{2} + cos^{2}x)/(cosx(1 +sinx)) = (1+2sinx +sin^{2}x +cos^{2}x)/(cosx*(1+sinx)) =

= (2 + 2 sinx)/(cosx*(1+sinx)) = 2(1+sinx)/(cosx (1+sinx)) = 2/cosx = 2 secx

2secx = 2secx

The identity is proved.

Let's consider the left part of the expression:

((1+sinx)

= (2 + 2 sinx)/(cosx*(1+sinx)) = 2(1+sinx)/(cosx (1+sinx)) = 2/cosx = 2 secx

2secx = 2secx

The identity is proved.

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