Having trouble with trigonometry, please help.

Prove the identity:

[tex]\csc(x)(1 + \sin(x)) = 1 + \csc(x)[/tex]

Remember that the cosecant is the reciprocal of the sine. CSC(x) = 1/SIN(x) .
Now operate on the left side, and see if you can make it look like the right side:
CSCx (1 + SINx)
Substitute for CSCx :
(1/SINx) (1 + SINx)
Multiply them:
1/SINx + SINx/SINx which is the same as 1/SINx + 1 which is the same as CSCx + 1 , and that's the right side of the identity, so you proved it.

Answered by AL2006 | 2024-06-10

We proved the identity csc ( x ) ( 1 + sin ( x )) = 1 + csc ( x ) by substituting csc ( x ) as s i n ( x ) 1 ​ and simplifying both sides to demonstrate they are equal. Therefore, the identity is confirmed. The final result shows that both sides are indeed the same expression.
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Answered by AL2006 | 2024-12-23