Fill in the blanks

(i) sin² θ cosec² θ = ……..

(ii) 1 + tan² θ = ……

(iii) Reciprocal sin θ. cot θ = ……

(iv) 1–.......= cos²θ

(v)

(vi)

(vii) cos θ is reciprocal of .........

(viii) Reciprocal of sin θ is.........

(ix) Value of sin θ in terms of cos θ is

(x) Value of cos θ in terms of sin θ is

(i) Given: sin² θ cosec² θ

= 1

(ii) Given: 1 + tan² θ

[∵ cos² θ + sin² θ = 1]

= sec² θ

(iii) Given : sin θ cot θ

Firstly, we simplify the given trigonometry

= cos θ

Now, the reciprocal of cos θ is

=sec θ

(iv) Given: 1 – x = cos²θ

Subtracting 1 to both the sides, we get

1 – x –1 = cos²θ – 1

⇒ –x = – sin²θ

⇒ x =sin² θ

(v)

(vi)

(vii)

(viii)

(ix) We know that

cos² θ + sin² θ = 1

⇒ sin² θ = 1 – cos² θ

⇒ sin θ = √(1 – cos² θ)

(x) We know that

cos² θ + sin² θ = 1

⇒ cos ² θ = 1 – sin² θ

⇒ cos θ = √(1 – sin² θ)