Advertisements
Advertisements
प्रश्न
If A + B + C = 180°, prove that sin A + sin B + sin C = `4 cos "A"/2 cos "B"/2 cos "C"/2`
उत्तर
L.H.S = (sin A + sin B) + sin C
= `2sin ("A" + "B")/2 cos(("A" - "B")/2) + 2sin "C"/2 cos "C"/2`
= `2cos "C"/2[cos(("A" - "B")/2) + sin "C"/2]`
= `2cos "C"/2[cos(("A" - "B")/2) + cos ("A" + "B")/2]`
= `2cos "C"/2[2cos "A"/2 cos "B"/2]`
= `4cos "A"/2 cos "B"/2 cos "C"/2`
= R.H.S
APPEARS IN
संबंधित प्रश्न
Find the values of cos(300°)
Find the value of the trigonometric functions for the following:
cos θ = `- 1/2`, θ lies in the III quadrant
Find the value of the trigonometric functions for the following:
tan θ = −2, θ lies in the II quadrant
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
Prove that sin(n + 1) θ sin(n – 1) θ + cos(n + 1) θ cos(n – 1)θ = cos 2θ, n ∈ Z
Prove that sin2(A + B) – sin2(A – B) = sin2A sin2B
Prove that cos 8θ cos 2θ = cos25θ – sin23θ
If θ is an acute angle, then find `cos (pi/4 + theta/2)`, when sin θ = `8/9`
If A + B = 45°, show that (1 + tan A)(1 + tan B) = 2
Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ
Show that `cot(7 1^circ/2) = sqrt(2) + sqrt(3) + sqrt(4) + sqrt(6)`
Show that `((cos theta -cos 3theta)(sin 8theta + sin 2theta))/((sin 5theta - sin theta) (cos 4theta - cos 6theta))` = 1
Prove that sin x + sin 2x + sin 3x = sin 2x (1 + 2 cos x)
Prove that `(sin x + sin 3x + sin 5x + sin 7x)/(cos x + cos x + cos 5x cos 7x)` = tan 4x
Prove that `(sin(4"A" - 2"B") + sin(4"B" - 2"A"))/(cos(4"A" - 2"B") + cos(4"B" - 2"A"))` = tan(A + B)
If A + B + C = 180°, prove that sin2A + sin2B − sin2C = 2 sin A sin B cos C
If A + B + C = 180°, prove that sin(B + C − A) + sin(C + A − B) + sin(A + B − C) = 4 sin A sin B sin C
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that sin2 B + sin2 C = 1
Choose the correct alternative:
`(1 + cos pi/8) (1 + cos (3pi)/8) (1 + cos (5pi)/8) (1 + cos (7pi)/8)` =
