Given 4 sin θ = 3 cos θ, find the values of : (i) sin θ (ii) cos θ (iii) cot 2 θ - cosec 2 θ

Let ABC be a triangle with ∠B = 90° and ∠C = θ. Given, ⇒ 4 sin θ = 3 cos θ ⇒ . ⇒ tan θ = ...........(1) From figure. ⇒ tan θ = ............(2) From (1) and (2) we get : Let AB = 3x and BC = 4x. In right angle triangle ABC, ⇒ AC 2 = AB 2 + BC 2 ⇒ AC 2 = (3x) 2 + (4x) 2 ⇒ AC 2 = 9x 2 + 16x 2 ⇒ AC 2 = 25x 2 ⇒ AC 2 = ⇒ AC = 5x. (i) By formula, ⇒ sin θ = . Hence, sin θ = . (ii) By formula, ⇒ cos θ = . Hence, cos θ = . (iii) By formula, ⇒ cot θ = . ⇒ cot 2 θ = = . ⇒ cosec θ = . ⇒ cosec 2 θ = = . Hence, cot 2 θ - cosec 2 θ = -1.

If q cos θ = p, find tan θ - cot θ in terms of p and q.

View Answer Bookmark Now

From the figure (2) given below, find the values of :
(i) 5 sin x
(ii) 7 tan x
(iii) 5 cos x - 17 sin y - tan x

View Answer Bookmark Now

Mathematics

Given 4 sin θ = 3 cos θ, find the values of :
(i) sin θ
(ii) cos θ
(iii) cot² θ - cosec² θ

Trigonometrical Ratios

Related Questions

If q cos θ = p, find tan θ - cot θ in terms of p and q.

From the figure (2) given below, find the values of :
(i) 5 sin x
(ii) 7 tan x
(iii) 5 cos x - 17 sin y - tan x

Mathematics

Given 4 sin θ = 3 cos θ, find the values of :(i) sin θ(ii) cos θ(iii) cot2 θ - cosec2 θ

Trigonometrical Ratios

Related Questions

If q cos θ = p, find tan θ - cot θ in terms of p and q.

From the figure (2) given below, find the values of :(i) 5 sin x(ii) 7 tan x(iii) 5 cos x - 17 sin y - tan x

Given 4 sin θ = 3 cos θ, find the values of :
(i) sin θ
(ii) cos θ
(iii) cot² θ - cosec² θ

From the figure (2) given below, find the values of :
(i) 5 sin x
(ii) 7 tan x
(iii) 5 cos x - 17 sin y - tan x