4. Write the reciprocal of cosec θ.
Step 1: Understand the definition of a reciprocal.
The reciprocal of a number or function is 1 divided by that number or function.
So, the reciprocal of cosec θ is cosecθ1.
Step 2: Recall the fundamental trigonometric identity for cosec θ.
The cosecant function is defined as the reciprocal of the sine function:
cosecθ=sinθ1
Step 3: Substitute this identity into the reciprocal expression.
cosecθ1=sinθ11
Step 4: Simplify the expression.
sinθ11=1×1sinθ=sinθ
The reciprocal of cosec θ is sinθ.
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