Question

sin Thita +cos Thita =√2 find all trigonometry ratio​

Answer 1

See in the attachment.

Step-by-step explanation:

Given:

sinø + cosø = √2

To find:

All Trigonometry Ratio

Solution:

$\sin+ \cos = \sqrt{2} \\ \\ \sin + \sqrt{1 - {sin}^{2} } = \sqrt{2} \\ \\ \sqrt{1 - { \sin}^{2} } = \sqrt{2} - \sin$

[Squaring both side]

$\sqrt{1 - { \sin}^{2} x} = \sqrt{2} - \sin x\\ \\({\sqrt{1 - { \sin}^{2}x } )}^{2} = (\sqrt{2} - \sin ) {}^{2}x \\ \\ 1 - { \sin}^{2} x= {( \sqrt{2}) }^{2}x - 2. \sin. x\sqrt{2} + { \sin }^{2}x \\ \\ - { \sin }^{2}x - { \sin }^{2}x =2 - 1 - 2 \sqrt{2} \sin \: x \\ \\ 0 = 2 { \sin \: }^{2} x - 2 \sqrt{2} \sin + 1 \\ \\ ( \sqrt{2} \sin x){}^{2} - 2. \sqrt{2}\sin \: x.1 + {1}^{2} = 0 \\ \\ ( \sqrt{2} \sin x- 1) {}^{2} = 0 \\ \\ \sqrt{2} \sin x- 1 = 0 \\ \\\sqrt{2} \sin x= 1 \\ \\ \sin x = \frac{1}{ \sqrt{2} } \\ \\ \sin \: x = \sin \: \:45 \\ \\ x\: = 45$

Therefore, All Trigonometry Ratio are tan 45° , cot 45° , cosec 45°, sec 45°, cos 45°, sin 45° .