devoncruz23
21.01.2021 •
Mathematics
Verify the trig identity: tan^2 theta + cot^2 theta / csc^2 theta = sec^2 theta
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Ответ:
See proof below
Step-by-step explanation:
In trigonometry identity
tan^2 theta = sin^2 theta /cos^2 theta
cot^2 theta = cos^2 theta/sin^2 theta
csc^2 theta = 1/sin^2 theta
Substitute into the expression
(sin^2 theta /cos^2 theta )+ (cos^2 theta/sin^2 theta)/1/sin^2 theta
= [sin^4theta + cos^4theta/cos^2 theta sin^2 theta]÷(1/sin^2 theta)
= 1/cos^2 theta sin^2 theta÷(1/sin^2 theta)
= 1/cos^2 theta sin^2 theta * sin^2 theta/1
= 1/cos^2theta
= sec^2theta (Proved!)
Ответ:
5 m+2 m
Step-by-step explanation:
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