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
Express each of the following as the product of sines and cosines:
sin 12x + sin 4x
Prove that:
sin 50° + sin 10° = cos 20°
Prove that:
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 \[\frac{\lambda + 1}{\lambda - 1}\]
Express the following as the sum or difference of sine or cosine:
`cos (7"A")/3 sin (5"A")/3`
Prove that:
tan 20° tan 40° tan 80° = `sqrt3`.
Prove that:
2 cos `pi/13` cos \[\frac{9\pi}{13} + \text{cos} \frac{3\pi}{13} + \text{cos} \frac{5\pi}{13}\] = 0
Evaluate-
cos 20° + cos 100° + cos 140°
