Question

find the value of :-
(i) tan 30° tan 60°
(ii) sin² 30°+cos²30+cot²45°
(iii)cos² 60° + sin² 30°​

Answer 1

Step-by-step explanation:

(1)1+3/√3

(2) 2

(3) 1/2

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Answer 2

Answer:

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$(i) \: tan30 \degree \: tan60 \degree$

$∴ \: \: tan30 \degree \: = \sqrt{3} \: \:,</p><p> tan60 \degree \: = \frac{1}{ \sqrt{3} }$

$= \sqrt{3} \times \frac{1}{ \sqrt{3} } = 1$

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$(ii) \: sin^{2} 30 \degree + {cos}^{2} 30 \degree + {cot}^{2}45 \degree$

$∴ (\: sin^{2} 30 \degree + {cos}^{2} 30 \degree = 1)$

$∴cot 45 \degree = 1$

$= 1 \times 1 = 1$

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$(iii) \: cos^{2} 60 \degree + {sin}^{2}30 \degree$

$∴cos60 \: = \frac{1}{2} ,</p><p></p><p></p><p>sin30 = \frac{1}{3}$

$( \frac{1}{2}) ^{2}+( \frac{1}{2})^{2} = \frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$

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