Advertisements
Advertisements
प्रश्न
If sin x = cos y, then x + y = 45° ; write true of false
पर्याय
True
False
उत्तर
sin x = cosy = sin`(x/2 – y )`
if x and y are acute angles,
x = `(x)/(2) – y`
x + y = `(x)/(2)`
∴ x + y = 45° is false.
APPEARS IN
संबंधित प्रश्न
Evaluate the following expression:
(i) `tan 60º cosec^2 45º + sec^2 60º tan 45º`
(ii) `4cot^2 45º – sec^2 60º + sin^2 60º + cos^2 90º.`
If x = 30°, verify that
(i) `\tan 2x=\frac{2\tan x}{1-\tan ^{2}x`
(ii) `\sin x=\sqrt{\frac{1-\cos 2x}{2}}`
Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°
sin 67° + cos 75°
Evaluate:
`2/3 (cos^4 30° - sin^4 45°) - 3(sin^2 60° - sec^2 45°) + 1/4 cot^2 30°`.
Evaluate: `4(sin^2 30 + cos^4 60^@) - 2/3 3[(sqrt(3/2))^2 . [1/sqrt2]^2] + 1/4 (sqrt3)^2`
Without using trigonometric tables, prove that:
cos54° cos36° − sin54° sin36° = 0
Express each of the following in terms of trigonometric ratios of angles lying between 0° and 45°.
sec78° + cosec56°
Find the value of:
tan2 30° + tan2 45° + tan2 60°
If A =30o, then prove that :
sin 2A = 2sin A cos A = `(2 tan"A")/(1 + tan^2"A")`
If tan (A + B) = 1 and tan(A-B)`=1/sqrt3` , 0° < A + B < 90°, A > B, then find the values of A and B.
find the value of :
3sin2 30° + 2tan2 60° - 5cos2 45°
Prove that:
cos 30° . cos 60° - sin 30° . sin 60° = 0
Prove that:
`((tan60° + 1)/(tan 60° – 1))^2 = (1+ cos 30°) /(1– cos 30°) `
Prove that:
4 (sin4 30° + cos4 60°) -3 (cos2 45° - sin2 90°) = 2
For any angle θ, state the value of: sin2 θ + cos2 θ
If `sqrt3` = 1.732, find (correct to two decimal place) the value of `(2)/(tan 30°)`
If A = B = 45° ,
show that:
cos (A + B) = cos A cos B - sin A sin B
If A = 30°;
show that:
(sinA - cosA)2 = 1 - sin2A
Without using tables, evaluate the following: sin60° sin30°+ cos30° cos60°
Without using tables, evaluate the following: sec30° cosec60° + cos60° sin30°.
Without using tables, evaluate the following: cosec330° cos60° tan345° sin290° sec245° cot30°.
Without using table, find the value of the following:
`(sin30° - sin90° + 2cos0°)/(tan30° tan60°)`
Without using tables, find the value of the following: `(4)/(cot^2 30°) + (1)/(sin^2 60°) - cos^2 45°`
Find the value of x in the following: `2sin x/(2)` = 1
Find the value of x in the following: `sqrt(3)`tan 2x = cos60° + sin45° cos45°
If A = 30° and B = 60°, verify that: `(sin("A" -"B"))/(sin"A" . sin"B")` = cotB - cotA
If sin(A - B) = `(1)/(2)` and cos(A + B) = `(1)/(2)`, find A and B.
Find the value of the following:
(sin 90° + cos 60° + cos 45°) × (sin 30° + cos 0° – cos 45°)
Verify cos3A = 4cos3A – 3cosA, when A = 30°