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The expression $(s in θ + cosec θ)^{2} + (cos θ + sec θ)^{2}$ simplifies to:

Competition practiceTrigonometry

A5 + ta $n^{2}$ θ + co $t^{2}$ θ
B9 + ta $n^{2}$ θ + co $t^{2}$ θ
C7 − ta $n^{2}$ θ − co $t^{2}$ θ
D7 + ta $n^{2}$ θ + co $t^{2}$ θ

Step-by-Step Solution

Expanding gives (si

n^{2}

θ + co

s^{2}

θ) + 4 + cose

c^{2}

θ + se

c^{2}

θ = 1 + 4 + (1 + co

t^{2}

θ) + (1 + ta

n^{2}

θ) = 7 + ta

n^{2}

θ + co

t^{2}

θ.

Answer: D) 7 + ta

n^{2}

θ + co

t^{2}

θ

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