+71 Use Trigonometric identities to simplify Trigonometric Expressions.
1. \(sin\theta +sin\theta cot^2 \theta \)
2. \((sin\theta -sin\theta cos^2 \theta )/sin^2 \theta \)
3. \((csc^2 \theta - cot^2 \theta )/cos\theta \)
4. \(sin\theta (csc\theta -sin\theta )\)
5.\(cosx+cosxtan^2 x\)
6.\(cos\theta csc\theta tan\theta \)
+128474 1. sin θ + sin θ cot^2 θ = sin θ (1 + cot^2 θ) = sin θ * csc^2θ = sinθ (1/sin^2θ) =
1/ sinθ = csc θ
2. (sin θ - sin θ cos^2 θ) / sin^2 θ = sin θ ( 1 - cos^2 θ) / sin^2 θ = sin θ ( sin^2θ) / sin^2θ =
sin θ
3. (csc^2 θ - cot^2θ) / cos θ = 1 / cos θ = sec θ
4. sin θ ( csc θ - sin θ ) = sin θ ( 1/sin θ - sin θ) = 1 - sin^2 θ = cos^2θ
5. cos x + cos x tan^2 x = cos x ( 1 + tan^2 x) = cos x * sec^2 x = cos x * 1 / cos^2 x =
1 / cos x = sec x
6. cosθ cscθ tan θ = cos θ * 1 /sin θ * sin θ / cos θ = 1
