Math  /  Trigonometry

QuestionSimplify the trigonometric expression. 1+sin(y)1+csc(y)\frac{1+\sin (y)}{1+\csc (y)}

Studdy Solution
Simplify the overall expression by multiplying by the reciprocal of the denominator:
1+sin(y)1+1sin(y)=(1+sin(y))×sin(y)sin(y)+1 \frac{1+\sin(y)}{1+\frac{1}{\sin(y)}} = (1+\sin(y)) \times \frac{\sin(y)}{\sin(y) + 1}
Notice that 1+sin(y)1 + \sin(y) in the numerator and sin(y)+1\sin(y) + 1 in the denominator are identical, so they cancel each other out:
1+sin(y)sin(y)+1=1 \frac{1+\sin(y)}{\sin(y) + 1} = 1
Thus, the simplified expression is:
sin(y) \boxed{\sin(y)}

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