हिंदी

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

Advertisements
Advertisements

प्रश्न

Prove the following:

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

योग
Advertisements

उत्तर

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
Trigonometric Functions of Allied Angels
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Trigonometry - 2 - Exercise 3.2 [पृष्ठ ४२]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 11 Maharashtra State Board
अध्याय 3 Trigonometry - 2
Exercise 3.2 | Q 2. (i) | पृष्ठ ४२

संबंधित प्रश्न

Find the value of:

sin 15°


Find the values of:

tan 105°


Find the value of sin 690°.


Find the value of :

sin (495°)


Find the value of :

cos (600°)


Find the value of :

tan (– 690°)


Find the value of :

sec 240°


Find the value of :

cot (– 1110°)


Prove the following:

`cos((3pi)/2 + x) cos(2pi + x)[cot((3pi)/2 - x) + cot(2pi + x)]` = 1


Prove the following:

sec 840° . cot (– 945°) + sin 600° tan (– 690°) = `3/2`


Prove the following:

`("cosec"(90^circ - x)sin(180^circ - x)cot(360^circ - x))/(sec(180^circ + x)tan(90^circ + x)sin(-x))` = 1


Prove the following:

`(sin^3(pi + x)sec^2(pi - x)tan(2pi - x))/(cos^2(pi/2 + x)sin(pi - x)"cosec"^2 - x)` = tan3x


Select the correct option from the given alternatives :

If sin θ = n sin (θ + 2α), then tan (θ + α) is equal to


Select the correct option from the given alternatives :

Let 0 < A, B < `pi/2` satisfying the equation 3 sin2A + 2 sin2B = 1 and 3 sin 2A − 2 sin 2B = 0 then A + 2B is equal to ______


Prove the following:

cos 36° = `(sqrt(5) + 1)/4`


Prove the following:

`tan  pi/8 = sqrt(2) - 1`


If f(x) = `(2"x" + 3)/(3"x" - 2)`, `"x" ≠ 2/3`, then the function fof is ____________.


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


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


The value of `2 cot^2(π/6) + 4 tan^2(π/6) - 3  "cosec"(π/6)` is ______.


If `cosA/3 = cosB/4 = 1/5, - π/2 < A < 0` and `- π/2 < B < 0`, then the value of 2 sin A + 4 sin B is ______.


The value of cos 480° sin 150° + sin 600° cos 390° is ______.


The value of `cos^2  π/16 + cos^2  (3π)/16 + cos^2  (5π)/16 + cos^2  (7π)/16` is ______.


sin2 17.5° + sin2 72.5° is equal to ______.


If cos θ = `- sqrt(3)/2` and sin α = `-3/5`, where θ does not and α lies in the third quadrant, then `(2 tan α + sqrt(3) tan θ)/(cot^2 θ + cos alpha)` is equal to ______.


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


cos 1° + cos 2° + cos 3° + ... + cos 180° 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 + sin B + sin C = 3, then cos A + cos B + cos C is equal to ______.


The value of sin 930° 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 ______.


cos2 5° + cos2 10° + cos2 15° + .... + cos2 85° + cos2 90° is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×