Maths / Introduction to Trigonometry / Trigonometric Identities

QUESTION

Prove that  $\dpi{120} \fn_jvn \large (sin\Theta +cosec\Theta )^2+(cos\Theta +sec\Theta )^2$ $\dpi{120} \fn_jvn \large =7+tan^2\Theta +cot^2\Theta$

EXPLANATION
Explain TypeExplanation Content
Text

$LHS=(sin\Theta +cosec\Theta )^2+(cos\Theta +sec\Theta )^2$

$=sin^2\Theta +cosec^2\Theta +2\: \: sin\Theta \: \: cosec\: \Theta +cos^2+sec^2\Theta +2\: \: cos\: \Theta \: \: sec\Theta$

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

$+2sin\Theta \times \frac {1}{sin\Theta }+2cos\Theta \times \frac {1}{cos\Theta }$

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

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

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