Advertisements
Advertisements
Question
ABC is an isosceles right-angled triangle. Assuming of AB = BC = x, find the value of each of the following trigonometric ratios: sin 45°
Solution
Given that AB = BC = x
∴ AC = `sqrt(AB^2+BC^2) = sqrt(x^2 + x^2) = xsqrt2`
sin 45° = `"AB"/"AC" = x/(xsqrt2) = 1/sqrt2`
APPEARS IN
RELATED QUESTIONS
Evaluate the following:
`(5cos^2 60° + 4sec^2 30° - tan^2 45°)/(sin^2 30° + cos^2 30°)`
Evaluate the following:
`(sin 20^@)/(cos 70^@)`
Evaluate the following :
`((sin 49^@)/(cos 41^@))^2 + (cos 41^@/(sin 49^@))^2`
Evaluate the following :
cosec 31° − sec 59°
Prove the following
sin θ sin (90° − θ) − cos θ cos (90° − θ) = 0
Evaluate: Cosec (65 + θ) – sec (25 – θ) – tan (55 – θ) + cot (35 + θ)
Prove that
cosec (67° + θ) − sec (23° − θ) = 0
Given A = 60° and B = 30°,
prove that : sin (A + B) = sin A cos B + cos A sin B
If A = B = 45° ,
show that:
sin (A - B) = sin A cos B - cos A sin B
find the value of: cos2 60° + sin2 30°
Prove that:
cosec2 45° - cot2 45° = 1
Prove that:
cos2 30° - sin2 30° = cos 60°
prove that:
tan (2 x 30°) = `(2 tan 30°)/(1– tan^2 30°)`
ABC is an isosceles right-angled triangle. Assuming of AB = BC = x, find the value of each of the following trigonometric ratios: tan 45°
If tan θ = cot θ and 0°∠θ ∠90°, state the value of θ
If sin x = cos y; write the relation between x and y, if both the angles x and y are acute.
If A = B = 45° ,
show that:
cos (A + B) = cos A cos B - sin A sin B
If A = 30°;
show that:
cos 2A = cos4 A - sin4 A
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: cosec245° sec230° - sin230° - 4cot245° + sec260°.
Without using table, find the value of the following:
`(sin30° - sin90° + 2cos0°)/(tan30° tan60°)`
Find the value of x in the following: tan x = sin45° cos45° + sin30°
If A = 30° and B = 60°, verify that: `(sin("A" -"B"))/(sin"A" . sin"B")` = cotB - cotA
If sin(A - B) = sinA cosB - cosA sinB and cos(A - B) = cosA cosB + sinA sinB, find the values of sin15° and cos15°.
If sin(A +B) = 1(A -B) = 1, find A and B.
Verify the following equalities:
cos 90° = 1 – 2sin2 45° = 2cos2 45° – 1
Verify the following equalities:
sin 30° cos 60° + cos 30° sin 60° = sin 90°
The value of `(1 - tan^2 45^circ)/(1 + tan^2 45^circ)` is
Evaluate: sin2 60° + 2tan 45° – cos2 30°.