if cosa= 7/8 then the value of (1+sin)(1-sin)/(1+cos)(1-cos)
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if cosa= 7/8 then the value of (1+sin)(1-sin)/(1+cos)(1-cos)
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Verified answer
Simplifying:
49/64/(sin^2(a))
Explanation:
To find the value of the expression (1+sin)(1-sin)/(1+cos)(1-cos) given that cosα = 7/8, we can substitute the value of cosα into the expression.
Let's break it down step by step:
1. Given: cosα = 7/8
2. Substitute the value of cosα into the expression:
(1+sinα)(1-sinα)/(1+cosα)(1-cosα)
3. Simplify the expression using the identity sin^2α + cos^2α = 1:
(1-sin^2α)/(1-cos^2α)
4. Substitute the values of sin^2α and cos^2α using the identity:
(1-(1-cos^2α))/(1-cos^2α)
5. Simplify the expression further:
(cos^2α)/(1-cos^2α)
6. Substitute the value of cosα = 7/8:
(7/8)^2/(1-(7/8)^2)
7. Calculate the expression:
(49/64)/(1-(49/64))
8. Simplify the expression:
(49/64)/(15/64)
9. Divide the numerator by the denominator:
49/15
Therefore, the value of the expression (1+sin)(1-sin)/(1+cos)(1-cos) when cosα = 7/8 is 49/15.Got it! You're looking to find the value of the expression (1+sin)(1-sin)/(1+cos)(1-cos) given that cos(a) = 7/8. To solve this, let's break it down step by step:
First, let's substitute the value of cos(a) into the expression:
(1+sin(a))(1-sin(a))/(1+cos(a))(1-cos(a))
Now, we can simplify the expression:
(1 - sin^2(a))/(1 - cos^2(a))
Using the Pythagorean identity sin^2(a) + cos^2(a) = 1, we can simplify it further:
(1 - sin^2(a))/(1 - (1 - sin^2(a)))
Simplifying even more:
(1 - sin^2(a))/(sin^2(a))
Since sin^2(a) + cos^2(a) = 1, we can replace cos^2(a) with 1 - sin^2(a):
(1 - sin^2(a))/(sin^2(a)) = (cos^2(a))/(sin^2(a))
Now, we can substitute the value of cos(a) = 7/8:
(7/8)^2/(sin^2(a))
Simplifying:
49/64/(sin^2(a))
And that's the simplified expression! If you provide me with the value of sin(a), I can help you calculate the final result. Let me know!
cos a = 7/8
(1+sin a)(1-sin a)/(1+cos a)(1-cos a)
=1-sin²a/1-cos²a
=cos²/sin². (since sin²+cos² =1 so 1-sin² = cos²)
=cot² a
cos =base / hypotenuse
now calculate the perpendicular side of the triangle by pythogoras theorem and put the value of base/ perpendicular
and then square it...
OK.