If cos theta =3/5, find the value of 5 cosec theta - 4 tan theta / sec theta + cot theta
Answers
Answered by
78
cos theta= adjacent /hypothenus
according to pythareous theorem, (hypotenuse)^2=(adj)^2+ (opp)^2
therefore, (5)^2 =(3)^2+x^2
X^2 = 25-9=16
x=4
cosec theta= hypotenuse/opposite = 5/4
tan theta= opposite/adjacent= 4/3
sec theta = hypotenuse/ adjacent= 5/3
cot theta = adjacent /opposite= 3/4
5 cosec theta- 4 tan theta = 5(5/4) - 4(4/3)=25/4-16/3= 11/12
sec theta+ cot theta= 5/3+ 3/4=29/12
5 cosec theta -4 tan theta/ sec theta + cot theta = (11/12)/(29/12)=11/29
according to pythareous theorem, (hypotenuse)^2=(adj)^2+ (opp)^2
therefore, (5)^2 =(3)^2+x^2
X^2 = 25-9=16
x=4
cosec theta= hypotenuse/opposite = 5/4
tan theta= opposite/adjacent= 4/3
sec theta = hypotenuse/ adjacent= 5/3
cot theta = adjacent /opposite= 3/4
5 cosec theta- 4 tan theta = 5(5/4) - 4(4/3)=25/4-16/3= 11/12
sec theta+ cot theta= 5/3+ 3/4=29/12
5 cosec theta -4 tan theta/ sec theta + cot theta = (11/12)/(29/12)=11/29
Answered by
41
Cos theta =3/5=adjacent/hypotenuse
Therefore opposite side=4(Pythagorean triplets)
Cosec theta = 5/4
Tan theta=4/3
Sec theta=5/3
Cot theta =3/4
5cosec theta-4 tan theta/sec theta+ cot theta
=(5*5/4-4/3)÷5/3+3/4
=25/4-16/3÷20+9/12
=75-64/12÷29/12
=11/12*12/29
=11/29
Hope this will help you
Similar questions