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1.	In ∆ABC, ∠C = 90°, ∠ABC =θ°, BC = 21 units and Ab = 29 unitsShow that : cos2– sin2 =\(\frac{41}{841}.\)
Answer» Given that AB = 29 units & BC = 21 units and ∠ABC =θ°& ∠ACB = 90°. Using Pythagoras theorem in right angled triangle ∆ACB, AB2 = AC2 + BC2 ⇒ AC2 = AB2 − BC2 ⇒ AC =\(\sqrt{AB^2-BC^2}\)=\(\sqrt{29^2-21^2}\)=\(\sqrt{841-441}=\sqrt{400}\) =20 units. (∵ BC = 21, AB = 29) Now, cosθ =\(\frac{BC}{AB}=\frac{21}{29}.\)(∵ BC = 21, AB = 29) And sinθ =\(\frac{AC}{AB}=\frac{20}{29}.\)(∵ AC = 20 and AB = 29) Now, cos2θ− sin2θ =\((\frac{21}{29})^2-(\frac{20}{29})^2\)=\(\frac{21^2-20^2}{29^2}\) =\(\frac{441 \,- \,400}{841}=\frac{41}{841}.\). Hence Proved

In ∆ABC, ∠C = 90°, ∠ABC =θ°, BC = 21 units and Ab = 29 unitsShow that : cos2– sin2 =\(\frac{41}{841}.\)

Answer»

Given that AB = 29 units & BC = 21 units and ∠ABC =θ°& ∠ACB = 90°.

Using Pythagoras theorem in right angled triangle ∆ACB,

AB2 = AC2 + BC2

⇒ AC2 = AB2 − BC2

⇒ AC =\(\sqrt{AB^2-BC^2}\)=\(\sqrt{29^2-21^2}\)=\(\sqrt{841-441}=\sqrt{400}\)

=20 units.

(∵ BC = 21, AB = 29)

Now, cosθ =\(\frac{BC}{AB}=\frac{21}{29}.\)(∵ BC = 21, AB = 29)

And sinθ =\(\frac{AC}{AB}=\frac{20}{29}.\)(∵ AC = 20 and AB = 29)

Now, cos2θ− sin2θ =\((\frac{21}{29})^2-(\frac{20}{29})^2\)=\(\frac{21^2-20^2}{29^2}\)

=\(\frac{441 \,- \,400}{841}=\frac{41}{841}.\).

Hence Proved

Discussion

2.	A student has set up a solar cooker in a box using a black painted aluminium sheet, a black cooking vessel, some glass wool , a transparent glass sheet and a mirror plate. What is the role of black paint, transparent glass sheet and a mirror used in the solar cooker ?
Answer» Black paint absorbs the heat energy quickly and thus helps in increasing the inner temperature. Glass sheet causes green-houses effect to retain the reflected infrared rays of heat, within the solar cooker. Mirror reflects the solar rays so that these rays reach inside the solar cooker.

Discussion

Explore topic-wise InterviewSolutions in .

In ∆ABC, ∠C = 90°, ∠ABC =θ°, BC = 21 units and Ab = 29 unitsShow that : cos2– sin2 =\(\frac{41}{841}.\)

A student has set up a solar cooker in a box using a black painted aluminium sheet, a black cooking vessel, some glass wool , a transparent glass sheet and a mirror plate. What is the role of black paint, transparent glass sheet and a mirror used in the solar cooker ?