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:
tan 20° tan 40° tan 60° tan 80° = 3
Prove that:
sin 50° − sin 70° + sin 10° = 0
Prove that:
Prove that:
sin 3A + sin 2A − sin A = 4 sin A cos \[\frac{A}{2}\] \[\frac{3A}{2}\]
Prove that:
cos 20° cos 100° + cos 100° cos 140° − 140° cos 200° = −\[\frac{3}{4}\]
Prove that:
The value of cos 52° + cos 68° + cos 172° is
Evaluate-
cos 20° + cos 100° + cos 140°
