Maths / Introduction to Trigonometry / Trigonometric Identities

QUESTION
 

If  cos: : Theta -sin: : Theta =sqrt {2}: : sin: : Theta , then  cos : : Theta +sin: : Theta =

OPTIONS
A. 

0

B. 

pm sqrt {2}: cos: : Theta

C. 

pm : :sqrt {2}: : sin: : Theta

D. 

1

Right Option : B

EXPLANATION
Explain TypeExplanation Content
Text

large cos: : Theta -sin: : Theta =sqrt {2}: : sin: : Theta ,

Squaring Both Sides

large cos^2Theta +sin^2Theta- 2;cos;Theta;sinTheta = 2;sin^2;Theta

large 1- 2;cos;Theta;sinTheta = 2;sin^2;Theta

large - 2;cos;Theta;sinTheta = 2;sin^2;Theta -1

large 2;cos;Theta;sinTheta = 1-2;sin^2;Theta

 

large (cos;Theta+sin;Theta)^2=cos^2Theta +sin^2Theta+2;cos;Theta;sinTheta

large (cos;Theta+sin;Theta)^2=1+1-2;sin^2Theta

large (cos;Theta+sin;Theta)^2=2-2;sin^2Theta

large (cos;Theta+sin;Theta)^2=2(1-;sin^2Theta)

large (cos;Theta+sin;Theta)^2=2(cos^2Theta)

large cos;Theta+sin;Theta=pm sqrt2;cosTheta

 

 

 

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