Question

if tan²45° -cos² 30° = x sin 45° cos45° then x =​

Answer 1

Answer:

1-3/4=x/√2.1/√2

1/4=x/2

therefore x=1/2

Answer 2

$\sf{{Solution:-}}$

$\sf{{tan^{2}45^{\circ}-cos^{2}=x sin45^{\circ}cos45^{\circ}}}$

$\sf{{We \ have \ to \ find \ the \ value \ of \ x:-}}$

$\sf{{(1)^{2}-}}$$(\sf\dfrac{\sqrt {3}}{2})^{2}$$\sf{{=x}}$$\sf\dfrac{1}{\sqrt{2}}$$(\sf\dfrac{1}{\sqrt {2}})$

$\implies \sf{{1-}}$$\sf\dfrac{3}{4}$$\sf{{=x}}$$(\sf\dfrac{1}{2})$

$\implies \sf\dfrac{4-3}{4}$$\sf{{=x}}$$(\sf\dfrac{1}{2})$

$\implies \sf\dfrac{1}{4}$$\sf{{=x}}$$(\sf\dfrac{1}{2})$

$\implies \sf{{x=}}$$\sf\dfrac{1}{4}$$\div\dfrac{1}{2}$

$\implies \sf{{x=}}$$\sf\dfrac{1}{4}$$\times\dfrac{2}{1}$

$\implies \sf{{x=}}$$\sf\dfrac{1}{2}$

$\sf{{Required \ Answer:-}}$

$\sf{{Value \ of \ x = }}$$\sf\dfrac{1}{2}$

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$\sf{{Trigonometry \ Table:-}}$

$\Large{ \begin{tabular}{|c|c|c|c|c|c|} \cline{1-6} \theta & \sf 0^{\circ} & \sf 30^{\circ} & \sf 45^{\circ} & \sf 65^{\circ} & \sf 90^{\circ} \\ \cline{1-6} \sin & 0 & \dfrac{1}{2 } & \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} & 1 \\ \cline{1-6} \cos & 1 & \dfrac{ \sqrt{ 3 }}{2} } & \dfrac{1}{ \sqrt{2} } & \dfrac{ 1 }{ 2 } & 0 \\ \cline{1-6} \tan & 0 & \dfrac{1}{ \sqrt{3} } & 1 & \sqrt{3} & \infty \\ \cline{1-6} \cot & \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } &0 \\ \cline{1 - 6} \sec & 1 & \dfrac{2}{ \sqrt{3}} & \sqrt{2} & 2 & \infty \\ \cline{1-6} \csc & \infty & 2 & \sqrt{2 } & \dfrac{ 2 }{ \sqrt{ 3 } } & 1 \\ \cline{1 - 6}\end{tabular}}$

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