Advertisements
Advertisements
प्रश्न
Find the value of cos 105°.
Advertisements
उत्तर
cos 105° = cos(60° + 45°)
= [cos 60° cos 45° – sin 60° sin 45°]
= `[1/2*1/sqrt2-sqrt(3)/2*1/sqrt(2)]`
= `(1-sqrt3)/(2sqrt2)`
APPEARS IN
संबंधित प्रश्न
Find the values of `tan ((19pi)/3)`
`(5/7, (2sqrt(6))/7)` is a point on the terminal side of an angle θ in standard position. Determine the six trigonometric function values of angle θ
Find sin(x – y), given that sin x = `8/17` with 0 < x < `pi/2`, and cos y = `- 24/25`, x < y < `(3pi)/2`
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
If a cos(x + y) = b cos(x − y), show that (a + b) tan x = (a − b) cot y
Prove that sin 75° – sin 15° = cos 105° + cos 15°
Prove that cos 8θ cos 2θ = cos25θ – sin23θ
Show that tan(45° + A) = `(1 + tan"A")/(1 - tan"A")`
Show that tan(45° − A) = `(1 - tan "A")/(1 + tan "A")`
Prove that `tan(pi/4 + theta) tan((3pi)/4 + theta)` = – 1
Prove that sin 4α = `4 tan alpha (1 - tan^2alpha)/(1 + tan^2 alpha)^2`
Show that `cot(7 1^circ/2) = sqrt(2) + sqrt(3) + sqrt(4) + sqrt(6)`
Show that sin 12° sin 48° sin 54° = `1/8`
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 x + sin 2x + sin 3x = sin 2x (1 + 2 cos x)
Prove that cos(30° – A) cos(30° + A) + cos(45° – A) cos(45° + A) = `cos 2"A" + 1/4`
If A + B + C = 180◦, prove that sin 2A + sin 2B + sin 2C = 4 sin A sin B sin C
If A + B + C = 180°, prove that sin A + sin B + sin C = `4 cos "A"/2 cos "B"/2 cos "C"/2`
Choose the correct alternative:
If `pi < 2theta < (3pi)/2`, then `sqrt(2 + sqrt(2 + 2cos4theta)` equals to
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
