Advertisements
Advertisements
प्रश्न
If A + B + C = 2s, then prove that sin(s – A) sin(s – B)+ sin s sin(s – C) = sin A sin B
Advertisements
उत्तर
Now sin(s – A) sin(s – B) = `1/2 {cos[("s" - "A") - ("s" - "B")] - cos[("s" - "A") + ("s" - "B")]}`
= `1/2cos("s" - "A" - "s" + "B") - cos[2"s" - ("A" + "B")]`
= `1/2 {cos("A" - "B) - cos"C"}` .....[∴ cos(A – B) = cos(B – A)]
Again sin s sin s – C = `1/2[cos"C" - cos("A" + "B")`
So, L.H.S = `1/2 {cos("A" - "B") - cos"C" + cos"C" - cos("A" + "B")}`
= `1/2 [cos("A" - "B") - cos("A" + "B")`
= `1/2 [2sin"A" sin"B"]`
= sin A sin B
= 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:
cos θ = `2/3`, θ lies in the I quadrant
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
Expand cos(A + B + C). Hence prove that cos A cos B cos C = sin A sin B cos C + sin B sin C cos A + sin C sin A cos B, if A + B + C = `pi/2`
Prove that sin 105° + cos 105° = cos 45°
Prove that cos(A + B) cos C – cos(B + C) cos A = sin B sin(C – A)
Prove that cos(A + B) cos(A – B) = cos2A – sin2B = cos2B – sin2A
Show that tan(45° + A) = `(1 + tan"A")/(1 - tan"A")`
If tan x = `"n"/("n" + 1)` and tan y = `1/(2"n" + 1)`, find tan(x + y)
Find the value of cos 2A, A lies in the first quadrant, when tan A `16/63`
If A + B = 45°, show that (1 + tan A)(1 + tan B) = 2
Express the following as a product
cos 35° – cos 75°
Show that `cos pi/15 cos (2pi)/15 cos (3pi)/15 cos (4pi)/15 cos (5pi)/15 cos (6pi)/15 cos (7pi)/15 = 1/128`
Prove that `sin theta/2 sin (7theta)/2 + sin (3theta)/2 sin (11theta)/2` = sin 2θ sin 5θ
Show that cot(A + 15°) – tan(A – 15°) = `(4cos2"A")/(1 + 2 sin2"A")`
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos B – cos C = `- 1 + 2sqrt(2) cos "B"/2 sin "C"/2`
Choose the correct alternative:
`1/(cos 80^circ) - sqrt(3)/(sin 80^circ)` =
Choose the correct alternative:
`(1 + cos pi/8) (1 + cos (3pi)/8) (1 + cos (5pi)/8) (1 + cos (7pi)/8)` =
Choose the correct alternative:
`(sin("A" - "B"))/(cos"A" cos"B") + (sin("B" - "C"))/(cos"B" cos"C") + (sin("C" - "A"))/(cos"C" cos"A")` is
