Question

)If sine + cose = √2cose, (e ≠ 90°) then the value of tane is a) √2 − 1 b) √2 + 1 c) √2 d) −√2 ​

Answer 1

√2 - 1

Step-by-step explanation:

=> sine + cose = √2 cose

Divide both sides by cos e:

=> (sine + cose)/cose = √2cose/cose

=> (sine/cose) + (cose/cose) = √2(1)

=> tane + 1 = √2

=> tane = √2 - 1

Method 2 :

=> sine + cose = √2 cose

=> sine = √2cose - cose

=> sine = cose (√2 - 1)

=> sine/cose = √2 - 1

=> tane = √2 - 1

Answer 2

Answer:

Given :-

• If sine + cose = √2cose, (e ≠ 90°)

To Find :-

• What is the value of tane.

Solution :-

$\dashrightarrow \sf sine + cose =\: \sqrt{2}cose$

By dividing both sides by cose :

$\implies \sf \dfrac{sine + cose}{cose} =\: \dfrac{\sqrt{2}\cancel{cose}}{\cancel{cose}}$

$\implies \sf \dfrac{sine}{cose} + \dfrac{\cancel{cose}}{\cancel{cose}} =\: \sqrt{2}$

$\implies \sf \dfrac{sine}{cose} + 1 =\: \sqrt{2}$

$\implies \sf tane + 1 =\: \sqrt{2}\: [\bold{\pink{\because\: \dfrac{sine}{cose} =\: tane}}]$

$\implies \sf tane + 1 =\: \sqrt{2}$

$\implies \sf tane =\: \sqrt{2} - 1$

$\implies \sf\bold{\red{tane =\: (\sqrt{2} - 1)}}$

$\sf\boxed{\bold{\purple{\therefore\: The\: value\: of\: tane\: is\: (\sqrt{2} - 1)\: .}}}$