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
Show that:
sin A sin (B − C) + sin B sin (C − A) + sin C sin (A − B) = 0
Prove that:
sin 38° + sin 22° = sin 82°
Prove that:
cos 55° + cos 65° + cos 175° = 0
Prove that:
If cos (α + β) sin (γ + δ) = cos (α − β) sin (γ − δ), prove that cot α cot β cot γ = cot δ
Write the value of sin \[\frac{\pi}{12}\] sin \[\frac{5\pi}{12}\].
If cos A = m cos B, then write the value of \[\cot\frac{A + B}{2} \cot\frac{A - B}{2}\].
Prove that:
sin (A – B) sin C + sin (B – C) sin A + sin(C – A) sin B = 0
