If sinø=4/5 find the value of cosecø/1+cotø
3,4,5 right triangle
so
sin = 4/5 so cosec = 5/4
tan = 4/3 so cot = 3/4
so
(5/4)/(1 + 3/4)
= 5/7
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To find the value of cosecø/1+cotø when sinø=4/5, we can start by determining the values of cosecø and cotø.
The reciprocal of sine is cosecant, so cosecø is the reciprocal of sinø. Therefore, cosecø = 1/sinø.
Given that sinø = 4/5, we can substitute this value into the equation to find cosecø:
cosecø = 1/(4/5) = 5/4
Now, let's find the value of cotø. Cotangent is the reciprocal of tangent, so cotø = 1/tanø.
To find cotø, we need to determine the value of tanø. To do this, we can use the Pythagorean identity, which states that:
sin²ø + cos²ø = 1
Given that sinø = 4/5, we can calculate cosø using this equation:
(4/5)² + cos²ø = 1
16/25 + cos²ø = 1
cos²ø = 1 - 16/25
cos²ø = 9/25
cosø = √(9/25) = 3/5
Now that we have the value of cosø, we can find tanø by dividing sinø by cosø:
tanø = sinø / cosø
tanø = (4/5) / (3/5)
tanø = 4/3
Finally, we can substitute the values of cosecø (5/4) and cotø (4/3) into the expression cosecø/1+cotø:
cosecø/1+cotø = (5/4)/(1 + 4/3)
To simplify further, we can multiply both the numerator and denominator by 12 to clear the fractions:
(5/4)/(1 + 4/3) = (5/4)*(3/3) / (1*(3/3) + 4/3)
= (15/12) / (3/3 + 4/3)
= (15/12) / (7/3)
= (15/12)*(3/7)
= (45/84)
= 15/28
Therefore, the value of cosecø/1+cotø when sinø = 4/5 is 15/28.