Question

cosQ + sinQ =1 ,show that cosQ - sinQ =1​

Answer 1

Step-by-step explanation:

cosQ+sinQ=1

squaring both sides

(cosQ+sinQ)²=1²

cos²Q+sin²Q+2sinQcosQ=1

1-sin²Q+1-cos²Q+2sinQcosQ=1

2-sin²Q-cos²Q+2sinQcosQ=1

-sin²Q-cos²Q+2cosQsinQ=-1

sin²Q+cos²Q-2sinQcosQ=1

(cosQ-sinQ)²=1

cosQ-sinQ=±1