cos cube theta minus Cos 3 theta upon cos theta + sin cube theta minus sin 3 theta upon sin theta is equal to 3
Answers
Trigonometry:
Trigonometry is the study of relations between angles and their ratios with various properties to find sine, cosine, tan, cosec, sec and cot ratios. Some properties can deduce angles in their general value apart from known definite ones. Now let us know some identities-
1. sin²θ + cos²θ = 1
2. sec²θ - tan²θ = 1
3. cosec²θ - cot²θ = 1
4. sin3θ = 3 sinθ - 4 sin³θ
5. cos3θ = 4 cos³θ - 3 cosθ
[ correcting the question ]
Proof:
Now, L.H.S.
L.H.S. = (cos³θ - cos3θ)/cosθ + (sin³θ + sin3θ)/sinθ
= (cos³θ - 4 cos³θ + 3 cosθ)/cosθ + (sin³θ + 3 sinθ - 4 sin³θ)/sinθ
= (- 3 cos³θ + 3 cosθ)/cosθ + (- 3 sin³θ + 3 sinθ)/sinθ
= - 3 cos²θ + 3 - 3 sin²θ + 3
= - 3 (cos²θ + sin²θ) + 6
= - 3 + 6
= 3
= R.H.S.
Hence, proved.
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