cot2θ−sin2θ1 is equal to :
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Step-by-Step Solution
Step 1: Recall trigonometric identities
We need to simplify the given expression. To do this, we will use fundamental trigonometric identities. First, recall that the cosecant function, cscθ, is the reciprocal of the sine function, sinθ. Also, there is a Pythagorean identity relating cot2θ and csc2θ.
Step 2: Substitute the reciprocal identity
Substitute the reciprocal identity sin2θ1=csc2θ into the original expression. This transforms the expression into a form that can be further simplified using another identity.
Step 3: Apply the Pythagorean identity
From the Pythagorean identity cot2θ+1=csc2θ, we can substitute csc2θ with (cot2θ+1) in our expression. This substitution is key to simplifying the expression to a constant value.
Step 4: Simplify the expression
Now, distribute the negative sign and combine like terms. The cot2θ terms cancel each other out, leaving us with a simple numerical result.