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Jul 8, 2025 · As we know that sinθ × sin (60° - θ) × sin (60° + θ) = 1/4 × sin3θ ---- (2) Now, from (1) and (2) equation sin10° × sin (60° - 10°) × sin (60° + 10°) × 1/2 1/4 × sin (3 × 10°) × 1/2 ⇒ 1/4 × …
So we can substitute this value into the equation: \ ( LHS = \sin 10^\circ \cdot \frac {1} {2} \cdot \sin 50^\circ \cdot \sin 70^\circ \) This simplifies to: \ ( LHS = \frac {1} {2} \sin 10^\circ \sin 50^\circ …
If y sin ϕ = x sin (2θ + ϕ), prove that (x + y) cot (θ + ϕ) = (y − x) cot θ.
Feb 6, 2021 · \ (\frac12 \times \sin10° \times \sin50° \times \sin 70°\) \ ( (\because \sin30° = \frac 12)\) \ (= \frac {1} {4} \times (2\sin10° \times \sin50°)\times \sin70°\)
Free math problem solver answers your trigonometry homework questions with step-by-step explanations.
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Using the product-to-sum formula, we can pair the sines: sin(10°)sin(70°) = 21[cos(10°−70°)−cos(10°+70°)] = 21[cos(−60°)−cos(80°)]= 21[cos(60°)−cos(80°)]
Mar 4, 2023 · We can use the identity sin (180 - x) = sin x to rewrite sin 170° as sin 10°: 16 sin 10° sin 30° sin 50° cos 20° = 8 sin 10° [2 cos 20° sin 30° sin 50°]
May 20, 2024 · To verify the identity \ ( \sin 10^\circ \sin 30^\circ \sin 50^\circ \sin 70^\circ = \frac {1} {16} \), we will use trigonometric identities and known values. Firstly, let's recall that \ ( \sin …
A physicist calculating the trajectory of a projectile launched at 60° with an initial velocity of 50 m/s can determine the horizontal and vertical components.
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