Question

In right angle triangle angle ABC, right angle at B, angle ACB= theta, AB = 2cm and BC= 1.evaluate sin^2theta + tan^2theta

Answer 1

Step-by-step explanation:

AB = 2 cm and BC = 1cm

Using Pythagoras theorem in ΔABC, we get,

AC² = AB² + BC²

AC² = 2² + 1 = 5

AC=√5

Thus, Base = BC = 1cm , Perpendicular = AB = 2cm and Hypotenuse = AC = √5cm

sinΦ = AB / AC = 2 /√5 and, tanΦ = AB / AC = 2 / 1 = 2

sin²Φ + tan²Φ = ( sinΦ )² + ( tanΦ)² = ( 2/√5 )² + (2)² = 4/5 + 4 = 24/5

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