Q. 15.0( 3 Votes )

Fill in the blanks

(i) sin2 θ cosec2 θ = ……..

(ii) 1 + tan2 θ = ……

(iii) Reciprocal sin θ. cot θ = ……

(iv) 1–.......= cos2θ



(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

Answer :

(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





(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)

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