English

ABC is an isosceles right-angled triangle. Assuming of AB = BC = x, find the value of each of the following trigonometric ratios: sin 45° - Mathematics

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°

Sum

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`

shaalaa.com
  Is there an error in this question or solution?
Chapter 23: Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios] - Exercise 23 (A) [Page 291]

APPEARS IN

Selina Concise Mathematics [English] Class 9 ICSE
Chapter 23 Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Exercise 23 (A) | Q 5.1 | Page 291

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°.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×