मराठी
तामिळनाडू बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान इयत्ता ११

Prove that coseccot(180∘+θ)sin(90∘-θ)cos(-θ)sin(270∘+θ)tan(-θ)cosec(360∘+θ) = cos2θ cotθ - Mathematics

Advertisements
Advertisements

प्रश्न

Prove that `(cot(180^circ + theta) sin(90^circ - theta) cos(- theta))/(sin(270^circ + theta) tan(- theta) "cosec"(360^circ + theta))` = cos2θ cotθ

बेरीज
Advertisements

उत्तर

`(cot(180^circ + theta) sin(90^circ - theta) * cos(- theta))/(sin(270^circ + theta) tan(- theta)  "cosec"(360^circ + theta))` 

= `(cot theta* costheta costheta)/(- cos theta xx - tantheta xx "cosec" theta)`

= `(cot theta * cos^2theta)/(cos theta tan theta  "cosec" theta)`

= `(cot theta * cos^2theta)/(cos theta * sintheta/costheta * 1/sin theta)`

= `cos^2theta * cottheta`

shaalaa.com
Trigonometric Functions and Their Properties
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Trigonometry - Exercise 3.3 [पृष्ठ १०४]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
पाठ 3 Trigonometry
Exercise 3.3 | Q 4 | पृष्ठ १०४

संबंधित प्रश्‍न

Find the values of sin (– 1110°)


Find the value of the trigonometric functions for the following:
cos θ = `- 1/2`, θ lies in the III quadrant


If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2` find the value of sin(x + y)


If sin A = `3/5` and cos B = `9/41 0 < "A" < pi/2, 0 < "B" < pi/2`, find the value of sin(A + B)


Find cos(x − y), given that cos x = `- 4/5` with `pi < x < (3pi)/2`  and sin y = `- 24/25` with `pi < y < (3pi)/2`


Find sin(x – y), given that sin x = `8/17` with 0 < x < `pi/2`, and cos y = `- 24/25`, x < y < `(3pi)/2`


Prove that sin(45° + θ) – sin(45° – θ) = `sqrt(2) sin θ`


If x cos θ = `y cos (theta + (2pi)/3) = z cos (theta + (4pi)/3)`. find the value of xy + yz + zx


Prove that sin2(A + B) – sin2(A – B) = sin2A sin2B


If cos(α – β) + cos(β – γ) + cos(γ – α) = `- 3/2`, then prove that cos α + cos β + cos γ = sin α + sin β + sin γ = 0


Find the value of cos 2A, A lies in the first quadrant, when cos A = `15/17`


Prove that sin 4α = `4 tan alpha (1 - tan^2alpha)/(1 + tan^2 alpha)^2`


Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ


Prove that (1 + sec 2θ)(1 + sec 4θ) ... (1 + sec 2nθ) = tan 2nθ


Express the following as a product
sin 50° + sin 40°


Prove that `sin  theta/2 sin  (7theta)/2 + sin  (3theta)/2 sin  (11theta)/2` =  sin 2θ sin 5θ


If A + B + C = 180◦, prove that sin 2A + sin 2B + sin 2C = 4 sin A sin B sin C


If A + B + C = 180°, prove that `tan  "A"/2  tan  "B"/2 + tan  "B"/2 tan  "C"/2 + tan  "C"/2 tan  "A"/2` = 1


Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to


Choose the correct alternative:
Let fk(x) = `1/"k" [sin^"k" x + cos^"k" x]` where x ∈ R and k ≥ 1. Then f4(x) − f6(x) = 


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×