Advertisements
Advertisements
प्रश्न
If cos A + cos B = `1/2` and sin A + sin B = `1/4`, prove that tan `(("A + B")/2) = 1/2`
Advertisements
उत्तर
Given that cos A + cos B = `1/2`
2 cos `(("A + B")/2) cos (("A - B")/2) = 1/2` ..(1)
Also given that sin A + sin B = `1/4`
2 sin `(("A + B")/2) cos (("A - B")/2) = 1/4` ..(2)
`(2) divide (1)` we get,
`(2 sin (("A + B")/2) cos (("A - B")/2))/(2 cos (("A + B")/2) cos (("A - B")/2)) = (1/4)/(1/2)`
tan `(("A + B")/2)` = `2/4`
∴ tan `(("A + B")/2) = 1/2`
APPEARS IN
संबंधित प्रश्न
Prove that:
sin 105° + cos 105° = cos 45°
Prove that:
Prove that:
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.
Write the value of \[\sin\frac{\pi}{15}\sin\frac{4\pi}{15}\sin\frac{3\pi}{10}\]
cos 40° + cos 80° + cos 160° + cos 240° =
The value of sin 78° − sin 66° − sin 42° + sin 60° is ______.
Express the following as the product of sine and cosine.
cos 2θ – cos θ
Prove that:
sin (A – B) sin C + sin (B – C) sin A + sin(C – A) sin B = 0
