Q56 of 268 Page 4

If cos θ +sin θ=1, prove that cos θ – sin θ = ± 1

Using the formula,

(a+b)² + (a – b)² = 2(a²+b²)

⇒ (cos θ +sin θ)² + (cos θ – sin θ)² = 2(cos²θ + sin² θ)

⇒ 1 + (cos θ – sin θ)² = 2(1)

⇒ (cos θ – sin θ)² = 2 –1

⇒ (cos θ – sin θ)² = 1

⇒ (cos θ – sin θ) =√1

⇒ (cos θ – sin θ) = ±1

If cosec A + cot A = 5, find the value of cos A.

If tan θ + sec θ = x, show that sin θ=

Find the value of the following :

(i) sin 30^o + cos 60^o

(ii) sin² 45^o+cos²45^o

(iii) sin 30^o + cos 60^o – tan45^o

(iv)

(v) tan 60^o x cos30^o

If θ = 45°, find the value of

(i)

(ii) cos² θ - sin² θ