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Question
If 2 sin A – 1 = 0, show that: sin 3A = 3 sin A – 4 sin3 A
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Solution
2 sin A − 1 = 0
`=> sin A = 1/2`
We know `sin 30^circ = 1/2`
So, A = 30°
L.H.S. = sin 3 A = sin 90° = 1
R.H.S. = 3 sin A – 4 sin3 A
= 3 sin 30° – 4 sin3 30°
= `3(1/2) - 4(1/2)^3`
= `3/2 - 1/2`
= 1
L.H.S. = R.H.S.
RELATED QUESTIONS
Prove the following trigonometric identities.
`(1 + sec theta)/sec theta = (sin^2 theta)/(1 - cos theta)`
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`1/(1 - sinA) + 1/(1 + sinA) = 2sec^2A`
Prove the following identities:
`1/(cosA + sinA) + 1/(cosA - sinA) = (2cosA)/(2cos^2A - 1)`
Prove the following identities:
`(1 + (secA - tanA)^2)/(cosecA(secA - tanA)) = 2tanA`
Write the value of `(sin^2 theta 1/(1+tan^2 theta))`.
If `cosec theta = 2x and cot theta = 2/x ," find the value of" 2 ( x^2 - 1/ (x^2))`
From the figure find the value of sinθ.
Prove that: (1+cot A - cosecA)(1 + tan A+ secA) =2.
sin4A – cos4A = 1 – 2cos2A. For proof of this complete the activity given below.
Activity:
L.H.S = `square`
= (sin2A + cos2A) `(square)`
= `1 (square)` .....`[sin^2"A" + square = 1]`
= `square` – cos2A .....[sin2A = 1 – cos2A]
= `square`
= R.H.S
Factorize: sin3θ + cos3θ
Hence, prove the following identity:
`(sin^3θ + cos^3θ)/(sin θ + cos θ) + sin θ cos θ = 1`
