Question

❶ Find the values of x, y and z in each of the case given below ⟼
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❷ Prove that –
If Cos∅ + Sin∅ √2Cos∅, Show that Cos∅ - Sin∅ = √2 Sin∅
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– Kindly Don't Spamm⚠️
– No Copied answers⚠️
– Answer with full solution
please
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Note (For 1st Question) :

• Figure is provided in the Attachment.​

Answer 1

❶

y = 45° (converse of alternate interior angle theorem)

z = 45° (alternate interior angle theorem)

x = 135° (exterior angle theorem)

❷

$\large\underline{\orange{\bf Given :-}}$

$\to\: \:\sf Cos\varnothing + Sin\varnothing = \sqrt{2} \: Cos\varnothing$

$\large\underline{\orange{\bf To \: Prove :-}}$

$\to\: \:\sf Cos\varnothing - Sin\varnothing = \sqrt{2}\:Sin\varnothing$

$\large\underline{\orange{\bf Solution :-}}$

$\sf Cos\varnothing + Sin\varnothing = \sqrt{2} \: Cos\varnothing$

$:\implies\sf Sin\varnothing = \sqrt{2} \: Cos\varnothing - Cos\varnothing$

$:\implies\sf Sin\varnothing = Cos\varnothing \: (\sqrt{2} - 1)$

$:\implies\sf Sin\varnothing = \dfrac{Cos\varnothing \: (\sqrt{2} -1) (\sqrt{2} + 1)}{(\sqrt{2} + 1)}$

$:\implies\sf Sin\varnothing = \dfrac{Cos\varnothing \: (2 -1)}{(\sqrt{2} + 1)}$

$:\implies\sf (\sqrt{2} + 1) \: Sin\varnothing = Cos\varnothing$

$:\implies\sf\sqrt{2} \: Sin\varnothing + Sin\varnothing = Cos\varnothing$

$:\implies\sf Cos\varnothing = \sqrt{2} \: Sin\varnothing + Sin\varnothing$

$:\implies\sf Cos\varnothing - Sin\varnothing = \sqrt{2} \: Sin\varnothing$

HENCE PROVED

Answer 2

Answer:

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