Maths / Introduction to Trigonometry / Trigonometric Identities

QUESTION
 

Prove that  large (sinTheta +cosecTheta )^2+(cosTheta +secTheta )^2 large =7+tan^2Theta +cot^2Theta

EXPLANATION
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Text

LHS=(sinTheta +cosecTheta )^2+(cosTheta +secTheta )^2

=sin^2Theta +cosec^2Theta +2: : sinTheta : : cosec: Theta +cos^2+sec^2Theta +2: : cos: Theta : : secTheta

=(sin^2Theta +cos^2Theta )+cosec^2Theta +sec^2Theta

                                                +2sinTheta times frac {1}{sinTheta }+2cosTheta times frac {1}{cosTheta }

=1+(1+cot^2Theta )+(1+tan^2Theta )+2+2

=7+tan ^2Theta +cot^2Theta =RHS

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