Advertisements
Advertisements
Question
If sin x = cos y, then x + y = 45° ; write true of false
Options
True
False
Solution
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
RELATED QUESTIONS
An equilateral triangle is inscribed in a circle of radius 6 cm. Find its side.
Using the formula, sin(A – B) = sinA cosB – cosA sinB, find the value of sin 15º
Evaluate the following:
`(sin 30° + tan 45° – cosec 60°)/(sec 30° + cos 60° + cot 45°)`
State whether the following is true or false. Justify your answer.
sin (A + B) = sin A + sin B
Evaluate cos 48° − sin 42°
Evaluate the following :
`tan 10^@/cot 80^@`
Evaluate the following :
`((sin 49^@)/(cos 41^@))^2 + (cos 41^@/(sin 49^@))^2`
Evaluate the following :
`tan 35^@/cot 55^@ + cot 78^@/tan 12^@ -1`
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°
sec 76° + cosec 52°
Prove that sin 48° sec 42° + cos 48° cosec 42° = 2
Prove the following
sin θ sin (90° − θ) − cos θ cos (90° − θ) = 0
Prove the following :
`(cos(90°−A) sin(90°−A))/tan(90°−A) - sin^2 A = 0`
Evaluate tan 35° tan 40° tan 50° tan 55°
Evaluate: `(2sin 68)/cos 22 - (2 cot 15^@)/(5 tan 75^@) - (8 tan 45^@ tan 20^@ tan 40^@ tan 50^@ tan 70^@)/5`
Evaluate: `(3 cos 55^@)/(7 sin 35^@) - (4(cos 70 cosec 20^@))/(7(tan 5^@ tan 25^@ tan 45^@ tan 65^@ tan 85^@))`
Evaluate: `sin 18^@/cos 72^@ + sqrt3 [tan 10° tan 30° tan 40° tan 50° tan 80°]`
Prove that
cosec (67° + θ) − sec (23° − θ) = 0
Express each of the following in terms of trigonometric ratios of angles lying between 0° and 45°.
cosec54° + sin72°
find the value of: sin 30° cos 30°
Prove that:
sin 60° = 2 sin 30° cos 30°
Prove that:
`((tan60° + 1)/(tan 60° – 1))^2 = (1+ cos 30°) /(1– cos 30°) `
If A = 30°;
show that:
(sinA - cosA)2 = 1 - sin2A
Without using tables, evaluate the following: (sin90° + sin45° + sin30°)(sin90° - cos45° + cos60°).
Prove that: `((cot30° + 1)/(cot30° -1))^2 = (sec30° + 1)/(sec30° - 1)`
Verify the following equalities:
sin2 60° + cos2 60° = 1
If sin 30° = x and cos 60° = y, then x2 + y2 is
The value of `(1 - tan^2 45^circ)/(1 + tan^2 45^circ)` is
The value of cos1°. cos2°. cos3°. cos4°....................... cos90° is ______.
