Q55 of 268 Page 4

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

tan θ+ sec θ = x

⇒ tan θ = x – sec θ

Squaring both sides, we get

⇒ tan² θ =(x – secθ)²

⇒ tan² θ = x² + sec²θ – 2xsec θ

⇒ sec² θ – 1 = x² + sec²θ – 2xsec θ [∵ 1+ tan² A = sec² A]

⇒ –1 – x² = –2xsecθ

Now,

tan θ = x – sec θ

= RHS

Hence Proved

If tan A + sec A = 3, find the value of sin A.

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

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

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