3 Trigo Questions

Prove sec 2A + tan 2A = (cos A + sin A)/ (cos A - sin A) Express this as a sum of 2 trigo functions 2(siny)(sin5y) Prove (sin2A)^2 - (sinA)^2 = (sinA)(sin3A)

Quick way of working out all trigonometric multiple angle formulae

The double angle formulae are easy to learn: Sin 2x = 2 sin x cos x Cos 2x = (cos x)^2 - (sin x)^2 but working out Cos 4x say in terms of cos x and sin x by using identities such as Cos(A + B) = Cos A Cos B - Sin A Sin B is laborious. However, there is a simple method to work out any multiple angle formula, using De Moivre's Theorem and Euler's relation.

Pythagorean Identities (a) (sin x)^2 + (cos x)^2 = 1 (b) 1 + (tan x)^2 = (sec x)^2 (c) 1 + (cot x)^2 = (cosec x)^2

Important Formulas and their Explanations (VI): Identities of Plane Trigonometry Pythagorean Relation Pythagorean Identities Pythagorean Identities ... click for more

height and distance

The angle of elevation of a cloud from a point X m above a lake is A and the angle of depression of its reflection in the lake is 45o. Find the height of cloud?

equation of the circle

Find an equation of the circle which touches the straight-lines x + y = 2 and x - y = 2 and Touches the circle x2 + y2 =1?