Maths / Introduction to Trigonometry / Trigonometric Identities

QUESTION
 

If    large sinTheta +cosTheta =sqrt{3}, then prove that   large tanTheta+cotTheta=1

EXPLANATION
Explain TypeExplanation Content
Text

sinTheta +cosTheta =sqrt{3}             (Given)

Or     (sinTheta +cosTheta)^3=3

Or      sin^2Theta +cos^2Theta +2sinTheta cosTheta =3

            2sinTheta cosTheta = 2            [because sin^2Theta +cos^2Theta =1]

Or sinTheta cosTheta = 1 = sin^2Theta +cos^2Theta

Or   1=frac{sin^2Theta +cos^2Theta }{sinTheta cosTheta }

Therefore, tanTheta + cotTheta = 1

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