Advertisements
Advertisements
Question
If sin x = cos y; write the relation between x and y, if both the angles x and y are acute.
Solution
sin x = cos y = sin (90° – y )
if x and y are acute angles,
x = 90° – y
⇒ x + y = 90
Hence x and y are complement angles
APPEARS IN
RELATED QUESTIONS
Find the value of x in the following :
tan 3x = sin 45º cos 45º + sin 30º
If tan (A + B) = `sqrt3` and tan (A – B) = `1/sqrt3`; 0° < A + B ≤ 90°; A > B, find A and B.
Evaluate the following in the simplest form: sin 60º cos 45º + cos 60º sin 45º
Evaluate the following :
`(sin 21^@)/(cos 69^@)`
Evaluate the following :
`((sin 27^@)/(cos 63^@))^2 - (cos 63^@/sin 27^@)^2`
Express each one of the following in terms of trigonometric ratios of angles lying between
0° and 45°
Sin 59° + cos 56°
Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°
tan 65° + cot 49°
Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°
cot 85° + cos 75°
If Sin 3A = cos (A – 26°), where 3A is an acute angle, find the value of A =?
Prove that sin 48° sec 42° + cos 48° cosec 42° = 2
Prove that `sin 70^@/cos 20^@ + (cosec 20^@)/sec 70^@ - 2 cos 20^@ cosec 20^@ = 0`
Evaluate: `4(sin^2 30 + cos^4 60^@) - 2/3 3[(sqrt(3/2))^2 . [1/sqrt2]^2] + 1/4 (sqrt3)^2`
Evaluate: `sin 50^@/cos 40^@ + (cosec 40^@)/sec 50^@ - 4 cos 50^@ cosec 40^@`
Evaluate: tan 7° tan 23° tan 60° tan 67° tan 83°
If cos 20 = sin 4 θ ,where 2 θ and 4 θ are acute angles, then find the value of θ
find the value of: sin 30° cos 30°
If A =30o, then prove that :
sin 2A = 2sin A cos A = `(2 tan"A")/(1 + tan^2"A")`
find the value of :
3sin2 30° + 2tan2 60° - 5cos2 45°
If A =30o, then prove that :
cos 2A = cos2A - sin2A = `(1 – tan^2"A")/(1+ tan^2"A")`
Prove that: sin60°. cos30° - sin60°. sin30° = `(1)/(2)`
Find the value of x in the following: cos2x = cos60° cos30° + sin60° sin30°
If A = 30° and B = 60°, verify that: `(sin("A" -"B"))/(sin"A" . sin"B")` = cotB - cotA
If A = B = 45°, verify that sin (A - B) = sin A .cos B - cos A.sin B
If sin(A +B) = 1(A -B) = 1, find A and B.
Verify cos3A = 4cos3A – 3cosA, when A = 30°
The value of `(1 - tan^2 45^circ)/(1 + tan^2 45^circ)` 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 ______.
Find the value of x if `2 "cosec"^2 30 + x sin^2 60 - 3/4 tan^2 30` = 10