English

Prove the following: cos(π+x)cos(-x)sin(π-x)cos(π2+x) = cot2x - Mathematics and Statistics

Advertisements
Advertisements

Question

Prove the following:

`(cos(pi + x) cos(-x))/(sin(pi - x)cos(pi/2 + x))` = cot2x

Sum
Advertisements

Solution

L.H.S. = `(cos(pi + x) cos(-x))/(sin(pi - x)cos(pi/2 + x))`

= `((-cosx)(cosx))/((sinx)(-sinx)`

= `cos^2x/sin^2x`

= cot2x

= R.H.S.

shaalaa.com
  Is there an error in this question or solution?
Chapter 3: Trigonometry - 2 - Exercise 3.2 [Page 42]

RELATED QUESTIONS

Find the values of:

cos 75°


Find the value of :

sin (495°)


Find the value of :

cos (600°)


Find the value of :

tan 225°


Find the value of :

tan (– 690°)


Find the value of:

sec (–855°) 


Find the value of :

cosec 780°


Prove the following:

cosθ + sin (270° + θ) − sin (270° − θ) + cos (180° + θ) = 0


Prove the following:

tan 20° tan 80° cot 50° = `sqrt(3)`


Prove the following:

sin 36° = `(sqrt(10 - 2sqrt(5)))/4`


Prove the following:

`tan  pi/8 = sqrt(2) - 1`


Prove the following:

tan6° tan42° tan66° tan78° = 1


Prove the following:

sin47° + sin61° − sin11° − sin25° = cos7°


If a = sin 175°+ cos 175°, then ______.


If θ = `(17π)/3` then, tan θ – cot θ = ______.


`(1 - 2[cos 60^circ - cos 80^circ])/(2 sin 10^circ)` = ______.


The value of sin 495° is ______.


The value of sin(– 1125°) is ______.


The value of `cos  π/8 + cos  (3π)/8 + cos  (5π)/8 + cos  (7π)/8` is ______.


If tan θ = `1/sqrt(7)`, then `(("cosec"^2θ - sec^2θ))/(("cosec"^2θ + sec^2θ))` is equal to ______.


In a ΔABC, if ∠A = `π/2`, then cos2 B + cos2 C is equal to ______.


If ΔABC is a right angled at C, then tan A + tan B is equal to ______.


If `sin A - sqrt(6) cos A = sqrt(7) cos A`, then `cos A + sqrt(6) sin A` is equal to ______.


In a ΔPQR, if 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P = 1, then ∠R is equal to ______.


The value of cos (270° + θ) cos (90° – θ) – sin (270° – θ) cos θ is ______.


The value of the expression sin6 θ + cos6 θ + 3 sin2 θ . cos2 θ is ______.


The value of cos(– 870°) is ______.


The value of `(cos(90^circ + θ) sec(-θ)tan(180^circ - θ))/(sec(360^circ - θ)sin(180^circ + θ)cot(90^circ - θ))` is ______.


cos 1°. cos 2°. cos 3° ...... cos 179° = ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×