SOLUTION: Sec^2 X csc X Divided by Sec^2 X + csc^2 X (Secant squared x times cosecant x over secant squared x plus cosecant squared x) Directions: use basic identities to change the

Question 835601: Sec^2 X csc X
Divided by
Sec^2 X + csc^2 X
(Secant squared x times cosecant x over secant squared x plus cosecant squared x)
Directions: use basic identities to change the expression to one with only sines and cosines then simplify to a basic trig function.
The answer is sinx but how?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Sec^2 X csc X
Divided by
Sec^2 X + csc^2 X
----------------------------
(1/cos^2)(1/sin)]/[1/cos^2+1/sin^2]
------
= [1/(cos^2*sin)]/[(cos^2+sin^2)/(cos^2*sin^2]
-------
= [1/(cos^2*sin)]/[1/(cos^2*sin^2)]
======
Invert the denominator and multiply to get:
= [cos^2*sin^2]/[cos^2*sin]
=====
= sin(x)
===================
Cheers,
Stan H.
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