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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. $cos\theta csc\theta tan\theta$

Mathrules Nov 29, 2019

CPhill · Answer 1 · 2019-11-29T09:44:05

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