Without Using Trigonometric Identity , Show that : Cos 2 25 ∘ + Cos 2 65 ∘ = 1 - Mathematics

Question

Without using trigonometric identity , show that :

$\cos^{2} 25^{\circ} + \cos^{2} 65^{\circ} = 1$

Sum

Solution

Consider $\cos^{2} 25^{\circ} + \cos^{2} 65^{\circ}$

⇒ $\cos^{2} (90^{\circ} - 65^{\circ}) + \cos^{2} 65^{\circ}$

⇒ $\sin^{2} 65^{\circ} + \cos^{2} 65^{\circ} = 1$

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Trigonometric Identities

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Q 3.04 Q 3.03 Q 3.05

Chapter 21: Trigonometric Identities - Exercise 21.3

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Chapter 21 Trigonometric Identities
Exercise 21.3 | Q 3.04

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Find the value of sin²θ + cos²θ

Solution:

In Δ ABC, ∠ABC = 90°, ∠C = θ°

AB² + BC² = $□$ .....(Pythagoras theorem)

Divide both sides by AC²

$\frac{{AB}^{2}}{{AC}^{2}} + \frac{{BC}^{2}}{{AC}^{2}} = \frac{{AC}^{2}}{{AC}^{2}}$

∴ $(\frac{{AB}^{2}}{{AC}^{2}}) + (\frac{{BC}^{2}}{{AC}^{2}}) = 1$

But $\frac{AB}{AC} = □ and \frac{BC}{AC} = □$

∴ $\sin^{2} θ + \cos^{2} θ = □$

Without Using Trigonometric Identity , Show that : Cos 2 25 ∘ + Cos 2 65 ∘ = 1 - Mathematics

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