Simplify tan((3pi)/4)^2-sec((3pi)/4)^2

Problem

tan^2((3*π)/4)−sec^2((3*π)/4)

Solution

1. Identify the trigonometric identity relating the tangent and secant functions.

tan^2(θ)+1=sec^2(θ)

2. Rearrange the identity to match the form of the given expression by subtracting sec^2(θ) and 1 from both sides.

tan^2(θ)−sec^2(θ)=−1

3. Substitute the specific angle θ=(3*π)/4 into the rearranged identity.

tan^2((3*π)/4)−sec^2((3*π)/4)=−1

Final Answer

tan^2((3*π)/4)−sec^2((3*π)/4)=−1

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