3. cotx- ,x lies in third quadrant.
Given trigonometric function is,
cot x = 3 4
Write the expression of Pythagorean identity.
cosec 2 x − cot 2 x = 1
Substitute the value of sec θ .
cosec 2 x − ( 3 4 ) 2 = 1 cosec 2 x = 1 + 9 16 cosec 2 x = 25 16 cosec x = ± 5 4
Only cosec x = − 5 4 lies in third quadrant.
Write the expression of reciprocal relation.
sin x = 1 cosec x sin x = − 4 5
And
tan x = 1 cot x tan x = 4 3
The expression for cos x is
cos x = sin x cot x
Substitute the values
cos x = ( − 4 5 ) ( 3 4 ) cos x = − 3 5
Write the expression of reciprocal relation.
sec x = 1 cos x sec x = − 5 3
Given trigonometric function is,
Write the expression of Pythagorean identity.
Substitute the value of
Only
Write the expression of reciprocal relation.
And
The expression for
Substitute the values
Write the expression of reciprocal relation.
