If cos x + cos y = 1/3 and sin x + sin y = 1/4, Find the Values of cos(x+y), sin(x+y) and tan(x+y)
Given cos x+cos y=1/3 and sin x+sin y=1/4, find cos(x+y), sin(x+y) and tan(x+y) using sum-to-product formulas and the tangent half-angle substitution.
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16 sin 20° sin 40° sin 80° Is Equal To
JEE Main 2022 PYQ: evaluate 16 sin20° sin40° sin80° using the identity sin(60°−θ) sinθ sin(60°+θ) = (sin3θ)/4.
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cot x = −5/√11, x∈(π/2,π) — Evaluate a Multi-Angle Trig Expression
Given cot x = −5/√11 with x in the second quadrant, evaluate (sin(11x/2))(sin6x−cos6x)+(cos(11x/2))(sin6x+cos6x) by collapsing it to sin(x/2)+cos(x/2).
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A Wheel Makes 360 Revolutions in 1 Minute. Find the Number of Radians It Turns Through in 1 Second
A wheel makes 360 revolutions in one minute. Find how many radians it turns through in 1 second, converting revolutions per minute into radians per second.
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The Value of 2sin(12°) − sin(72°)
Evaluate 2sin(12°)−sin(72°) by splitting 72° as 60°+12°, then recombining into a single sine of a difference angle using sin18°.
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If sin x + sin²x = 1, x ∈ (0, π/2), Then (cos¹²x + tan¹²x) + 3(cos¹⁰x + tan¹⁰x + cos⁸x + tan⁸x) + (cos⁶x + tan⁶x) Is Equal To
Given sinx+sin²x=1 for x in (0,π/2), evaluate a large trigonometric expression by first proving tanx=cosx, then spotting a binomial cube pattern.