Maths / Introduction to Trigonometry / Trigonometric Identities

QUESTION
 

If  large cos: : Theta +sin: : Theta =sqrt {2}: : cos: : : Theta ,: : Find: : the;value ;of : : cos: : Theta -sin: : Theta

OPTIONS
A. 

large =sqrt {2}: : cos: : Theta .

B. 

large =sqrt {2}: : tan: : Theta .

C. 

large =sqrt {2}: : sin: : Theta .

D. 

None of these

Right Option : C

EXPLANATION
Explain TypeExplanation Content
Text

We have,

         cos: : : Theta +sin: : Theta =sqrt {2}: : cos : : Theta

Rightarrow : : : : : : : (cos: : : Theta +sin: : Theta )^2=2cos^2Theta

Rightarrow : : : : : : : cos^2Theta +sin^2Theta =2cos: : Theta : : cos: : Theta =2cos^2: Theta

Rightarrow : : : : : : : cos^2: Theta -2: : cos: : Theta : : sin: : : Theta =sin^2Theta

Rightarrow : : : : : : : cos^2Theta -2: : cos: : Theta : : sin: : Theta +sin^2Theta =2: : : sin^2: : Theta

Rightarrow : : : : : : : (cos: : Theta -sin: : : Theta )^2=2: : sin^2: : Theta

Rightarrow : : : : : : : cos: : Theta -sin: : Theta =sqrt {2}: : sin: : Theta

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