In ΔABC. if angle B=90°, BC=7 cm and (AC-AB)=1 cm then find the value of (cos A-sin A).. Created by swarooppaul111.

In ΔABC. if angle B=90°, BC=7 cm and (AC-AB)=1 cm then find the value of (cos A-sin A).

July 2023 1 3 Report

In ΔABC. if angle B=90°, BC=7 cm and (AC-AB)=1 cm then find the value of (cos A-sin A).

Answer:

Step-by-step explanation:

Let BC=xcm.then,AC=(x+1)cm.

By Pythagoras's theorem, we have

AB2+BC2=AC2

⇒72+x2=(x+1)2

⇒49+x2=(x−1)2

⇒49+x2=x2+2x+1

⇒2x=48

⇒x=24.

∴BC=24cm,AC=25cmandAB=7cm.

For T-ratios of ∠A, we have

sinA=BCAC=2425andcosA=ABAC=725.

For T- ratios of ∠C, we have

sinC=ABAC=725andcosC=BCAC=2425.