The value of 1+cot2θ1+tan2θ is :
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Step-by-Step Solution
Step 1: Apply trigonometric identities
We use the fundamental trigonometric identities: 1+tan2θ=sec2θ and 1+cot2θ=csc2θ. Substituting these into the given expression simplifies it.
Step 2: Express in terms of sine and cosine
Next, we express sec2θ and csc2θ in terms of sinθ and cosθ. We know that secθ=cosθ1 and cscθ=sinθ1.
Step 3: Simplify the complex fraction
To simplify the complex fraction, we multiply the numerator by the reciprocal of the denominator. This results in cos2θsin2θ.
Step 4: Convert to tangent
Finally, we recognize that cosθsinθ=tanθ. Therefore, the expression simplifies to tan2θ.