Question

the minimun value of cos thita -sin thita
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Answer 1

Answer:

the minimum value ofcos thita -sin thita is 0

Answer 2

TO FIND:-

$minimum \: value \: of = sin \: \theta - \: cos \: \theta$

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SOLUTION:-

LET SEE THE SIN@ AND COS@ TABLE:-

$\bullet \sf Trigonometric Values \\\\\\ \boxed{\begin{array}{c|c|c|c|c|c} \sf Angle & 0^{\circ} & 30^{\circ} & 45^{\circ} & 60^{\circ} & 90^{\circ} \\ \cline{1-6} \sin \theta & 0 & \dfrac{1}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{\sqrt{3}}{2} & 1 \\ \cline{1-6} \cos \theta & 1 & \dfrac{\sqrt{3}}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{1}{2} & 0 \\ \cline{1-6} \tan\theta & 0 & \dfrac{1}{\sqrt{3}} & 1 & \sqrt{3} & \textsf{Not D{e}fined}\end{array}}$

We observed that while moving from left to right value of Sin@ increase while Value of Cos@ decreased.

Substitute @ with 0°

Sin0°-Cos0°

$0 - 1 = - 1$

Substitute @ with 30°

Sin30°-Cos30°

$\dfrac{1}{2} - \dfrac{ \sqrt{3} }{2} = - 0.366$

Substitute @ with 45°

Sin45°-Cos45°

$\frac{1}{ \sqrt{2} } - \frac{1}{ \sqrt{2} } = 0$

Substitute @ with 60°

Sin60°- Cos60°

$\dfrac{ \sqrt{3} }{2} - \dfrac{1}{2} = 0.366$

Substitute @ with 90°

Sin90°-Cos90°

1-0=1

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HENCE LEAST VALUE OF SIN@ - COS@ IS.

-1...........ANSWER