Advertisements
Advertisements
प्रश्न
If A = B = 60°, verify that: cos(A - B) = cosA cosB + sinA sinB
Advertisements
उत्तर
cos(A - B) = cosA cosB + sinA sinB
L.H.S. :
cos(60° - 60°) = cos0° = 1
R.H.S. :
cosA cosB + sinA sinB
= cos60° cos60° + sin60° sin60°
= `(1)/(2) xx (1)/(2) + sqrt(3)/(2) xx sqrt(3)/(2)`
= `(1)/(4) + (3)/(4)`
= `(4)/(4)`
= 1
L.H.S. = R.H.S.
Therefore,
cos(A - B) = cosA cosB + sinA sinB.
APPEARS IN
संबंधित प्रश्न
If 2 sin x° − 1 = 0 and x° is an acute angle; find:
- sin x°
- x°
- cos x° and tan x°.
If sin x + cos y = 1 and x = 30°, find the value of y
Use the given figure to find:
(i) tan θ°
(ii) θ°
(iii) sin2θ° - cos2θ°
(iv) Use sin θ° to find the value of x.
Find the value of 'A', if 2 sin 2A = 1
If ΔABC is a right triangle such that ∠C = 90°, ∠A = 45° and BC =7units, find ∠B, AB and AC.
Find the value of 'y' if `sqrt(3)` = 1.723.
Given your answer correct to 2 decimal places.
Find the value of 'y' if `sqrt(3)` = 1.723.
Given your answer correct to 2 decimal places.
In the given figure, if tan θ = `(5)/(13), tan α = (3)/(5)` and RS = 12m, find the value of 'h'.
In the given figure, a rocket is fired vertically upwards from its launching pad P. It first rises 20 km vertically upwards and then 20 km at 60° to the vertical. PQ represents the first stage of the journey and QR the second. S is a point vertically below R on the horizontal level as P, find:
a. the height of the rocket when it is at point R.
b. the horizontal distance of point S from P.
Evaluate the following: `(5sec68°)/("cosec"22°) + (3sin52° sec38°)/(cot51° cot39°)`
