Question

from the adjacent figure, find the values of
I)sin² theta+cos²theta
ii)sec²theta-tan²theta
iii)cosec²theta-cot²theta​

Answer 1

answer:

1. sin²x+cos²x

• sinx=opposite side/hypothenuse side=3/5
• cosx=adjacent side/hypothenuse side=4/5
• sin²x=(3/5)²=9/25
• cos²x=(4/5)²=16/25
• according to question,
• 9/25+16/25
• 25/25
• 1

2.sec²x-tan²x

• sec x=hypothenuse side/adjacent side=5/4
• tan x=opposite side/adjacent side=3/4
• sec²x=(5/4)²=25/16
• tan²x=(3/4)²=9/16
• according to question,
• 25/16-9/16
• 16/16
• 1

3.cosec²x-cot²x

• cosec x=hypothenuse side/opposite side=5/3
• cot x=adjacent side/opposite side=4/3
• cosec²x=(5/3)²=25/9
• cot²x=(4/3)²=16/9
• according to question,
• 25/9-16/9
• 9/9
• 1