UPSC CDS 2 2022 Math Paper

Pythagoras theorem: In a right-angled theorem,
Hypotenuse 2= Base 2+ Perpendicular ‌2

We have, AB=12‌cm,BC=9‌cm,AC=15‌cm
122+92=144+81=225=152
Hence, △ABC is a right-angled triangle in which ∠C=90∘
As we know, ∠A+∠B+∠C=180∘ ⇒∠A+∠B=90∘‌‌(∵∠C=90∘) ⇒∠A=90∘−∠B

Now, the required value
cos2A+cos2B+cos2C‌
⇒cos2A+cos2(90∘−A)+cos290∘
⇒cos2A+sin2A+0‌[∵cos‌90∘=0]
⇒1+0‌[∵sin2θ+cos2θ=1]