Simplify $sin θ (csc θ + sin θ {sec}^{2} θ)$ $sintheta(csctheta+sinthetasec^2theta)$ ?

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Answer 1 · 2017-05-08T04:30:29

Please see below.

$sin θ (csc θ + sin θ {sec}^{2} θ)$ $sintheta(csctheta+sinthetasec^2theta)$

= $sin θ (\frac{1}{sin θ} + sin θ \times \frac{1}{{cos}^{2} θ})$ $sintheta(1/sintheta+sinthetaxx1/cos^2theta)$

= $1 + \frac{{sin}^{2} θ}{{cos}^{2} θ}$ $1+sin^2theta/cos^2theta$

= $1 + {tan}^{2} θ$ $1+tan^2theta$

= ${sec}^{2} θ$ $sec^2theta$

Simplify sintheta(csctheta+sinthetasec^2theta)sinθ(cscθ+sinθsec2θ)sintheta(csctheta+sinthetasec^2theta)?