Advertisements
Advertisements
प्रश्न
Prove that sin 105° + cos 105° = cos 45°
Advertisements
उत्तर
sin 105° + cos 105° = sin(90° + 15°) + cos(90° + 15°)
= cos 15° – sin 15°
= cos(45° – 30°) sin(45° – 30°)
= (cos 45° . cos30° + sin 45° sin 30°) – (sin 45° cos 30° – cos 45° sin 30°)
= `(1/sqrt(2) * sqrt(3)/2 + 1/sqrt(2) * 1/sqrt(2)) - (1/sqrt(2) * sqrt(3)/2 - 1/sqrt(2) * 1/sqrt(2))`
= `sqrt(3)/(2sqrt(2)) + 1/(2sqrt(2)) - sqrt(3)/(2sqrt(2)) + 1/(2sqrt(2))`
= `2/(2sqrt(2))`
= `1/sqrt(2)`
= cos 45°
APPEARS IN
संबंधित प्रश्न
Find the values of cos(300°)
Find the values of tan(1050°)
Find the value of the trigonometric functions for the following:
cos θ = `2/3`, θ lies in the I quadrant
Prove that `(cot(180^circ + theta) sin(90^circ - theta) cos(- theta))/(sin(270^circ + theta) tan(- theta) "cosec"(360^circ + theta))` = cos2θ cotθ
Find all the angles between 0° and 360° which satisfy the equation sin2θ = `3/4`
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 sin(π + θ) = − sin θ.
Prove that sin(30° + θ) + cos(60° + θ) = cos θ
Prove that sin 75° – sin 15° = cos 105° + cos 15°
Prove that sin2(A + B) – sin2(A – B) = sin2A sin2B
If cos(α – β) + cos(β – γ) + cos(γ – α) = `- 3/2`, then prove that cos α + cos β + cos γ = sin α + sin β + sin γ = 0
Show that tan(45° + A) = `(1 + tan"A")/(1 - tan"A")`
Find the value of cos 2A, A lies in the first quadrant, when cos A = `15/17`
If cos θ = `1/2 ("a" + 1/"a")`, show that cos 3θ = `1/2 ("a"^3 + 1/"a"^3)`
Express the following as a sum or difference
sin 5θ sin 4θ
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`
Show that `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` = tan 2x
If A + B + C = 180°, prove that `tan "A"/2 tan "B"/2 + tan "B"/2 tan "C"/2 + tan "C"/2 tan "A"/2` = 1
Choose the correct alternative:
`1/(cos 80^circ) - sqrt(3)/(sin 80^circ)` =
