Question

without using calculator, find the value for cos(150 °-45 °) in terms of surd​

Answer 1

$\red{ Value \: of \: cos ( 150 - 45) \degree }$

$= Cos 105\degree \\= Cos ( 60 + 45 )\degree$

/* We know that */

$\boxed{ \pink{ Cos (A+B) = Cos ACos B - Sin A Sin B }}$

$= Cos 60\degree Cos 45\degree - Sin 60\degree Sin 45\degree \\= \frac{1}{2} \times \frac{1}{\sqrt{2}} - \frac{\sqrt{3}}{2} \times \frac{1}{\sqrt{2}} \\= \frac{1}{2\sqrt{2}} - \frac{\sqrt{3}}{2\sqrt{2}} \\= \frac{ 1 - \sqrt{3}}{ 2\sqrt{2}}$

Therefore.,

$\red{ Value \: of \: cos ( 150 - 45) \degree }$

$\green { = \frac{ 1 - \sqrt{3}}{ 2\sqrt{2}}}$

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Answer 2

Answer:

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