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

(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

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


(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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