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10 cards from this deck
Understand the identity, simplify, and apply identities.
Examine the identity and decide which side to simplify.
Start with the side that looks more complex.
sin2θ+cos2θ=1\sin^2\theta + \cos^2\theta = 1sin2θ+cos2θ=1; 1+tan2θ=sec2θ1 + \tan^2\theta = \sec^2\theta1+tan2θ=sec2θ; csc2θ=1+cot2θ\csc^2\theta = 1 + \cot^2\thetacsc2θ=1+cot2θ.
Combine into one fraction and factor where applicable.
Convert all functions to sine and cosine for clarity.
Conclude with 'LHS=RHSLHS = RHSLHS=RHS' to confirm identity is proven.
It equals 111, derived from Pythagorean theorem.
It simplifies to 111 using trigonometric identities.
sin(2θ)=2sin(θ)cos(θ)\sin(2\theta) = 2\sin(\theta)\cos(\theta)sin(2θ)=2sin(θ)cos(θ).
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