# 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)

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