Find- the- value- of- sin-2 - - cos-2 -at- - 30-amp- 60-1-4- 3-43-4- 1-41- 10- 3-4

The correct option is C 1, 1At θ = 30°, sin 30°=1/2 and cos 30°=√(3)/2. Now, sin^230°+cos^230° =(1/2)^2 + (√(3)/2)^2 =1/4 +3/4 = 1. nbsp; Similarly, at ...

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Question

$F i n d t h e v a l u e o f s i n^{2} θ + c o s^{2} θ a t θ = 30^{\circ} & 60^{\circ}$ .

\frac{1}{4}, \frac{3}{4}

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\frac{3}{4}, \frac{1}{4}

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1, 1

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0, \frac{3}{4}

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Solution

The correct option is C $1, 1$
$A t θ = 30 °, s i n 30 ° = \frac{1}{2} a n d c o s 30 ° = \frac{\sqrt{3}}{2} . N o w, s i n^{2} 30 ° + c o s^{2} 30 ° = (\frac{1}{2})^{2} + (\frac{\sqrt{3}}{2})^{2} = \frac{1}{4} + \frac{3}{4} = 1.$

Similarly,
$a t θ = 60 °, s i n 60 ° = \frac{\sqrt{3}}{2} a n d c o s 30 ° = \frac{1}{2} . N o w, s i n^{2} 60 ° + c o s^{2} 60 ° = (\frac{\sqrt{3}}{2})^{2} + (\frac{1}{2})^{2} = \frac{3}{4} + \frac{1}{4} = 1.$

Hence, the value of $s i n^{2} θ + c o s^{2} θ a t θ = 30^{\circ} & 60^{\circ} i s 1.$

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Find the value of sin2θ+cos2θ at θ=30∘ & 60∘.

The correct option is C 1,1At θ=30°,sin 30°=12 and cos 30°=√32.Now, sin230°+cos230°=(12)2 + (√32)2=14+34=1. Similarly, at θ=60°,sin 60°=√32 and cos 30°=12.Now, sin260°+cos260°=(√32)2 + (12)2=34+14=1. Hence, the value of sin2θ+cos2θ at θ=30∘ & 60∘ is 1.

$F i n d t h e v a l u e o f s i n^{2} θ + c o s^{2} θ a t θ = 30^{\circ} & 60^{\circ}$ .