Q20 of 805 Page 427

If sec θ + tan θ = m, show that = sin θ.

Given sec θ + tan θ = m

So, we can write

Squaring both sides we get

Since cos² θ = 1- sin² θ

⇒

Applying Componendo & Dividendo i.e.

is equivalent to

we get

Hence Proved

If α, β are the zeros of the polynomial (x² - x - 12), then form a quadratic equation whose zeros are 2α and 2β.

Prove that (sin θ + cosec θ)² + (cos θ + sec θ)² = 7 + tan² θ + cot²θ.

In a trapezium ABCD, O is the point of intersection of AC and BD, AB|| CD and AB = 2 x CD. If area of ΔAOB = 84 cm², find the area of ΔCOD.

In the given figure, AB ⊥ BC, GF ⊥ BC and DE ⊥ AC. Prove that ΔADE ~ Δ GCF.