Advertisements
Advertisements
Question
Evaluate the following
cos 60° cos 45° - sin 60° ∙ sin 45°
Advertisements
Solution
cos 60° cos 45° - sin 60° ∙ sin 45° …(i)
By trigonometric ratios we know that,
`cos 60^@ = 1/2 cos 45^@ = 1/sqrt2`
`sin 60^@ = sqrt3/2 sin 45^@ = 1/sqrt2`
By substituting above value in (i), we get
`1/2. 1/sqrt2 - sqrt3/2. 1/sqrt2 => (1 - sqrt3)/(2sqrt2)`
APPEARS IN
RELATED QUESTIONS
In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determine:
sin A, cos A
If sin A = `3/4`, calculate cos A and tan A.
In ΔPQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.
State whether the following are true or false. Justify your answer.
cos A is the abbreviation used for the cosecant of angle A.
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cos theta = 7/25`
If sin θ = `12/13`, Find `(sin^2 θ - cos^2 θ)/(2sin θ cos θ) × 1/(tan^2 θ)`.
Evaluate the following
sin2 30° + sin2 45° + sin2 60° + sin2 90°
Evaluate the Following
`(sin 30^@ - sin 90^2 + 2 cos 0^@)/(tan 30^@ tan 60^@)`
Find the value of x in the following :
`2 sin x/2 = 1`
In ΔABC is a right triangle such that ∠C = 90° ∠A = 45°, BC = 7 units find ∠B, AB and AC
3 sin² 20° – 2 tan² 45° + 3 sin² 70° is equal to ______.
The value of the expression (sin 80° – cos 80°) is negative.
A ladder rests against a vertical wall at an inclination α to the horizontal. Its foot is pulled away from the wall through a distance p so that its upper end slides a distance q down the wall and then the ladder makes an angle β to the horizontal. Show that `p/q = (cos β - cos α)/(sin α - sin β)`
What will be the value of sin 45° + `1/sqrt(2)`?
In the given figure, if sin θ = `7/13`, which angle will be θ?
If sec θ = `1/2`, what will be the value of cos θ?
If sin θ + cos θ = `sqrt(2)` then tan θ + cot θ = ______.
Find an acute angle θ when `(cos θ - sin θ)/(cos θ + sin θ) = (1 - sqrt(3))/(1 + sqrt(3))`
If θ is an acute angle and sin θ = cos θ, find the value of tan2 θ + cot2 θ – 2.
If sin θ – cos θ = 0, then find the value of sin4 θ + cos4 θ.
