If sec A-tanA=5, then sinA=
Share
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Answer:
12/13
Step-by-step explanation:
Given, secA - tanA = 5 ...(1)
We know, sec²A - tan²A = 1.
⇒ sec²A - tan²A = 1
⇒ (secA + tanA)(secA - tanA) = 1
⇒ (secA + tanA)(5) = 1
⇒ secA + tanA + 1/5 ...(2)
Adding (1) and (2),
⇒ 2secA = 5 + 1/5
⇒ 2secA = (25+1)/5 = 26/5
⇒ secA = 13/5
⇒ 1/cosA = 13/5
⇒ cosA = 5/13
Thus,
sinA = √1 - cos²A = √1 - (5/13)²
= (13² - 5²)/13²
= √(144/169)
= 12/13