Advertisements
Advertisements
Question
If A = B = 60°, verify that: cos(A - B) = cosA cosB + sinA sinB
Advertisements
Solution
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
RELATED QUESTIONS
If sin 3A = 1 and 0 < A < 90°, find cos 2A
Solve for 'θ': `sin θ/(3)` = 1
If A = B = 60°, verify that: sin(A - B) = sinA cosB - cosA sinB
Find the value 'x', if:
Find x and y, in each of the following figure:
Find x and y, in each of the following figure:
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: sin31° - cos59°
Evaluate the following: `(3sin^2 40°)/(4cos^2 50°) - ("cosec"^2 28°)/(4sec^2 62°) + (cos10° cos25° cos45° "cosec"80°)/(2sin15° sin25° sin45° sin65° sec75°)`
Evaluate the following: `(5cot5° cot15° cot25° cot35° cot45°)/(7tan45° tan55° tan65° tan75° tan85°) + (2"cosec"12° "cosec"24° cos78° cos66°)/(7sin14° sin23° sec76° sec67°)`
