Simplify: cos θ |\table \cos\theta,\sin\theta;-\sin\theta,\cos\theta| + sin θ |\table \sin\theta,-\cos\theta;\cos\theta,\sin\theta|

CBSE Class 12 Math 2012 Solved Paper - Question 8

Question : 8 of 29

Marks: +1, -0

Simplify: cos θ

|\table cosθ,sinθ;-sinθ,cosθ|

+ sin θ

|\table sinθ,-cosθ;cosθ,sinθ|

Solution:

cos θ

|\table cosθ,sinθ;-sinθ,cosθ|

+ sin θ

|\table sinθ,-cosθ;cosθ,sinθ|

|\table cos^2θ,cosθsinθ;-sinθcosθ,cos^2θ|

|\table sin^2θ,-sinθcosθ;sinθcosθ,sin^2θ|

|\table cos^2θ+sin^2θ , cosθsinθ-sinθcosθ;-sinθcosθ+cosθsinθ,cos^2θ+sin^2θ|

|\table 1,0;0,1|

[Since

cos^2θ+sin^2θ

= 1]

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