If cos theta = 1/2 Find sec square theta + tan square theta / 7-2 sec theta cosec theta
Answers
Answer:
We can begin by using the trigonometric identities to simplify the expression. The trigonometric identities that relate the reciprocal trigonometric functions (cosec, sec, and cot)
Step-by-step explanation:
The essential trigonometric functions (sin, cos, and tan) are:
cosec(θ) = 1/sin(θ), sec(θ) = 1/cos(θ), and cot(θ) = 1/tan(θ)
Using these identities, we can rewrite the expression as:
sec^2(θ) + tan^2(θ) / (7-2*(1/cos(θ))*(1/(sin(θ))))
Now we know that cos(θ) = 1/2. We can substitute this value into the expression and simplify it further:
sec^2(θ) + tan^2(θ) / (7-22(1/(sin(θ))))
sec^2(θ) + tan^2(θ) / (7-8*(1/(sin(θ))))
sec^2(θ) + tan^2(θ) / (7-8*(1/(sqrt(1-1/4))))
sec^2(θ) + tan^2(θ) / (7-8*(2/sqrt(3)))
sec^2(θ) + tan^2(θ) / (7-16/sqrt(3))
We can further simplify the expression, but to get the final answer, we need the value of sin(theta)
It's important to note that this is the final simplified form of the given expression.
To learn more about trigonometry, find the given link.
https://brainly.in/question/2685053
To learn more about reciprocal trigonometry, find the given link.
https://brainly.in/question/5107227
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