English

If sinθ = cosθ and 0° < θ<90°, find the value of 'θ'. - Mathematics

Advertisements
Advertisements

Question

If sinθ = cosθ and 0° < θ<90°, find the value of 'θ'.

Sum

Solution

sinθ = cosθ

⇒ `"sinθ"/"cosθ" = "cosθ"/"cosθ"`
⇒  tanθ = 1
⇒  tanθ = tan45°
⇒ θ = 45°.

shaalaa.com
  Is there an error in this question or solution?
Chapter 27: Trigonometrical Ratios of Standard Angles - Exercise 27.1

APPEARS IN

Frank Mathematics [English] Class 9 ICSE
Chapter 27 Trigonometrical Ratios of Standard Angles
Exercise 27.1 | Q 9

RELATED QUESTIONS

If A, B and C are interior angles of a triangle ABC, then show that `\sin( \frac{B+C}{2} )=\cos \frac{A}{2}`


If tan (A + B) = `sqrt3` and tan (A – B) = `1/sqrt3`; 0° < A + B ≤ 90°; A > B, find A and B.


Evaluate the following:

`(cos 45°)/(sec 30° + cosec  30°)`


Evaluate the following:

`(5cos^2 60° +  4sec^2 30° - tan^2 45°)/(sin^2 30° +  cos^2 30°)`


`(1- tan^2 45°)/(1+tan^2 45°)` = ______


sin 2A = 2 sin A is true when A = ______.


Evaluate cos 48° − sin 42°


Evaluate the following

`sec 11^@/(cosec 79^@)`


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°

sec 76° + cosec 52°


Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°

cot 85° + cos 75°


Evaluate tan 35° tan 40° tan 50° tan 55°


Prove that

tan (55° − θ) − cot (35° + θ) = 0


Find the value of:

tan2 30° + tan2 45° + tan2 60°


If sin x = cos x and x is acute, state the value of x


If `sqrt3` = 1.732, find (correct to two decimal place)  the value of sin 60o


find the value of: cosec2 60° - tan2 30°


find the value of: sin2 30° + cos2 30°+ cot2 45°


find the value of :

3sin2 30° + 2tan2 60° - 5cos2 45°


Prove that:

3 cosec2 60°  - 2 cot2 30°  + sec2 45°  = 0


Without using tables, evaluate the following: sec30° cosec60° + cos60° sin30°.


Without using tables, find the value of the following: `(sin30°)/(sin45°) + (tan45°)/(sec60°) - (sin60°)/(cot45°) - (cos30°)/(sin90°)`


Find the value of x in the following: `sqrt(3)`tan 2x = cos60° + sin45° cos45°


If sin(A - B) = sinA cosB - cosA sinB and cos(A - B) = cosA cosB + sinA sinB, find the values of sin15° and cos15°.


Find the value of the following:

sin2 30° – 2 cos3 60° + 3 tan4 45°


If 2 sin 2θ = `sqrt(3)` then the value of θ is 


If sin α = `1/2`, then find the value of (3 cos α – 4 cos3 α).


Evaluate: `(5  "cosec"^2  30^circ - cos 90^circ)/(4 tan^2 60^circ)`


Find the value of x if `2 "cosec"^2 30 + x sin^2 60 - 3/4 tan^2 30` = 10


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×