Given sin θ = p/q , find cos θ + sin θ in terms of p and q.

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Let ABC be a right angle triangle with ∠C = θ and ∠B = 90°. By formula, sin θ = ........(1) Given, sin θ = .........(2) From (1) and (2) we get, Let AB = px and AC = qx. In right angled triangle ABC, By pythagoras theorem, ⇒ AC² = AB² + BC² ⇒ BC² = AC² - AB² ⇒ BC² = (qx)² - (px)² ⇒ BC² = q²x² - p²x² ⇒ BC² = x²(q² - p²) ⇒ BC = ⇒ BC = In right angled triangle ABC, By formula, cos θ = = . Substituting values in cos θ + sin θ we get, Hence, cos θ + sin θ =

Mathematics

Given sin θ = p/q , find cos θ + sin θ in terms of p and q.

Trigonometrical Ratios

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