Advertisements
Advertisements
प्रश्न
Without using tables, evaluate the following: (sin90° + sin45° + sin30°)(sin90° - cos45° + cos60°).
उत्तर
(sin90° + sin45° + sin30°)(sin90° - cos45° + cos60°).
sin30° = `(1)/(2)`
sin45° = `(1)/sqrt(2)`
sin90° = 1
cos45° = `(1)/sqrt(2)`
cos60° = `(1)/(2)`
(sin90° + sin45° + sin30°)(sin90° - cos45° + cos60°)
= `(1 + 1/sqrt(2) + 1/sqrt(2))(1 - 1/sqrt(2) + 1/sqrt(2))`
= `(3/2 + 1/sqrt(2))(3/2 - 1/sqrt(2))`
= `(3/2)^2 - (1/sqrt(2))^2`
= `(9)/(4) - (1)/(2)`
= `(9 - 2)/(4)`
= `(7)/(4)`.
APPEARS IN
संबंधित प्रश्न
If θ is an acute angle and sin θ = cos θ, find the value of 2 tan2 θ + sin2 θ – 1
Using the formula, sin(A – B) = sinA cosB – cosA sinB, find the value of sin 15º
Evaluate the following:
`(sin 20^@)/(cos 70^@)`
Evaluate the following
sec 50º sin 40° + cos 40º cosec 50º
Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°
cos 78° + sec 78°
Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°
cot 85° + cos 75°
Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°
sin 67° + cos 75°
If A, B, C are the interior angles of a triangle ABC, prove that
`tan ((C+A)/2) = cot B/2`
Prove that tan 20° tan 35° tan 45° tan 55° tan 70° = 1
Prove the following
`(tan (90 - A) cot A)/(cosec^2 A) - cos^2 A =0`
Prove the following :
`(cos(90°−A) sin(90°−A))/tan(90°−A) - sin^2 A = 0`
Evaluate:
`2/3 (cos^4 30° - sin^4 45°) - 3(sin^2 60° - sec^2 45°) + 1/4 cot^2 30°`.
If `sqrt3` = 1.732, find (correct to two decimal place) the value of sin 60o
If A = B = 45° ,
show that:
sin (A - B) = sin A cos B - cos A sin B
Prove that:
cos 30° . cos 60° - sin 30° . sin 60° = 0
prove that:
cos (2 x 30°) = `(1 – tan^2 30°)/(1+tan^2 30°)`
If sec A = cosec A and 0° ∠A ∠90°, state the value of A
If A =30o, then prove that :
sin 3A = 3 sin A - 4 sin3A.
If A = 30°;
show that:
4 cos A cos (60° - A). cos (60° + A) = cos 3A
Without using tables, evaluate the following: sin60° sin30°+ cos30° cos60°
Prove that : cos60° . cos30° - sin60° . sin30° = 0
Find the value of x in the following: cos2x = cos60° cos30° + sin60° sin30°
If tan `"A" = (1)/(2), tan "B" = (1)/(3) and tan("A" + "B") = (tan"A" + tan"B")/(1 - tan"A" tan"B")`, find A + B.
Verify the following equalities:
sin2 60° + cos2 60° = 1
Find the value of 8 sin 2x, cos 4x, sin 6x, when x = 15°
If 2 sin 2θ = `sqrt(3)` then the value of θ is
If sin(A + B) = 1 and cos(A – B)= `sqrt(3)/2`, 0° < A + B ≤ 90° and A > B, then find the measures of angles A and B.
The value of 5 sin2 90° – 2 cos2 0° is ______.
