If in ∆ABC, ∠C = 90° and tan A = 3/4 , prove that sin A cos B + cos A sin B = 1.

Question

KnowledgeBoat · Accepted Answer

Let ABC be a right angled triangle with ∠C = 90°. Given, tan A = By formula, ⇒ Let BC = 3x and AC = 4x. In △ABC, ⇒ AB² = AC² + BC² ⇒ AB² = (4x)² + (3x)² ⇒ AB² = 16x² + 9x² ⇒ AB² = 25x² ⇒ AB = ⇒ AB = 5x. By formula, Substituting values in L.H.S. of sin A cos B + cos A sin B = 1. Since, L.H.S. = R.H.S. Hence, proved that sin A cos B + cos A sin B = 1.

Mathematics

If in ∆ABC, ∠C = 90° and tan A = 3/4 , prove that sin A cos B + cos A sin B = 1.

Trigonometrical Ratios

Related Questions

Prove the following :
sin θ cot θ = cos θ

In the figure (2) given below, ∆ABC is right-angled at B and BD is perpendicular to AC. Find :
(i) cos ∠CBD
(ii) cot ∠ABD

Mathematics

If in ∆ABC, ∠C = 90° and tan A = 3/4 , prove that sin A cos B + cos A sin B = 1.

Trigonometrical Ratios

Related Questions

Prove the following :sin θ cot θ = cos θ

In the figure (2) given below, ∆ABC is right-angled at B and BD is perpendicular to AC. Find :(i) cos ∠CBD(ii) cot ∠ABD

Prove the following :
sin θ cot θ = cos θ

In the figure (2) given below, ∆ABC is right-angled at B and BD is perpendicular to AC. Find :
(i) cos ∠CBD
(ii) cot ∠ABD