Question

Evaluate sin power2 30+ cos power2 60+tan power2 90

Answer 1

sin30 =1/2
sin^2 30 =1/4
cos60=1/2
cos^2 60 =1/4
tan90 =infinity
tan^2 90 =infinity
now
1/4 +1/4 +infinity
2/4 +infinity
1/2 +infinity
0.5+infinity
= infinity is answer

Answer 2

Answer :

Let us know some trigonometric functions values

$\begin{center}\begin{tabular}{ |c|c|c|c|c|c|c|} \cline{1-7}\theta & sin\: \theta & cos \: \theta & tan \: \theta & cosec \: \theta & sec\: \theta & cot\: \theta \\0^{\circ} & 0 & 1 & 0 & inf. & 1 & inf. \\ 30^{\circ} & 1/2 & \sqrt{3}/2 & 1/\sqrt{3} & 2 & 2/\sqrt{3} & \sqrt{3}\\ 45^{\circ} & 1/\sqrt{2} & 1/\sqrt{2} & 1 & \sqrt{2} & \sqrt{2} & 1\\ 60^{\circ} & \sqrt{3}/2 & 1/2 & \sqrt{3} & 2/\sqrt{3} & 2 & 1/\sqrt{3}\\ 90^{\circ} & 1 & 0 & inf. & 1 & inf. & 0\\ \cline{1-7}\end{tabular}$

where inf. = infinity = ∞

Now, sin²30° + cos²60° + tan²90°

$= {(\frac{1}{2})}^{2} + {(\frac{1}{2})}^{2}$ + ∞²

= ∞

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