Advertisements
Advertisements
प्रश्न
Express the following as the sum or difference of sine or cosine:
cos(60° + A) sin(120° + A)
उत्तर
cos(60° + A) sin(120° + A)
`= 1/2` [2 cos(60° + A) sin(120° + A)] ....[Multiply and divide by 2]
= `1/2` [sin((60° + A) + (120° + A))] – sin((60° + A) – (120° + A))] ....[∵ 2 cos A sin B = sin(A + B) – sin(A – B)]
= `1/2` [sin(180° + 2A) – sin(60° + A – 120° – A)]
= `1/2` [(-sin 2A) – sin(-60°)]
= `1/2` [-sin 2A + sin 60°]
= `1/2 [-sin 2"A" + sqrt3/2]`
APPEARS IN
संबंधित प्रश्न
Prove that:
sin 20° sin 40° sin 80° = \[\frac{\sqrt{3}}{8}\]
Prove that:
tan 20° tan 40° tan 60° tan 80° = 3
If (cos α + cos β)2 + (sin α + sin β)2 = \[\lambda \cos^2 \left( \frac{\alpha - \beta}{2} \right)\], write the value of λ.
If cos A = m cos B, then write the value of \[\cot\frac{A + B}{2} \cot\frac{A - B}{2}\].
If sin 2A = λ sin 2B, then write the value of \[\frac{\lambda + 1}{\lambda - 1}\]
If cos (A + B) sin (C − D) = cos (A − B) sin (C + D), then write the value of tan A tan B tan C.
If sin (B + C − A), sin (C + A − B), sin (A + B − C) are in A.P., then cot A, cot B and cot Care in
Express the following as the sum or difference of sine or cosine:
`cos (7"A")/3 sin (5"A")/3`
Express the following as the product of sine and cosine.
sin 6θ – sin 2θ
Prove that:
`(cos 2"A" - cos 3"A")/(sin "2A" + sin "3A") = tan "A"/2`
