Question

The value of (tan square 45 degree - cos square 60 degree) is: options are - A) 1/2 B) 1/4 C) 3/2 D) 3/4​

Answer 1

Answer:

(D) 3/4 is the required answer .

Step-by-step explanation:

$\bf\;tan^{2}45^{\circ}- cos^{2} 60^{\circ}$

$\sf\dashrightarrow\; tan^{2}45^{\circ}- cos^{2} 60^{\circ} \\\\\\\sf\dashrightarrow\; (1)^{2} - (\frac{1}{2})^{2}\\\\\sf\dashrightarrow\; 1 - (\frac{1}{4})\\\\\\\sf\dashrightarrow\; 1 - \frac{1}{4}\\\\\\\sf\dashrightarrow\; \frac{4-1}{4} \\\\\\\sf\dashrightarrow\; \frac{3}{4} \\\\\\\boxed{\bf{Hence, the \; required \; option \; is \; D) \frac{3}{4}}}$

Additional Information !!

$\boxed{\begin{array}{c |c|c|c|c|c} \bf\angle\theta & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin \theta & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: theta & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan\theta & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec\theta & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec\theta & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot \theta & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0\end{array}}$

Answer 2

tan²45° - cos²60° = ¾

Step-by-step explanation:

$\rm➠\: \: { \tan}^{2} 45 \degree - { \cos}^{2} 60 \degree$

$\rm➠\: \: (1) ^{2} - {( \frac{1}{2})}^{2}$

$\rm➠\: \: 1 - \frac{1}{4}$

$\rm➠\: \: \frac{3}{4}$