prove that -
(cosec A - sin A) (sec A - cos A) = 1/(tan A + cot A).
Answers
Answered by
1
Answer:
LHS=(cosecA−sinA)(secA−cosA)=(
sinA
1
−sinA)(
cosA
1
−cosA)
=(
sinA
1−sin
2
A
)(
cosA
1−cos
2
A
)=sinAcosA=
2
1
sin2A
RHS=
tanA+cotA
1
=
1+tan
2
A
tanA
=
2
1
sin2A
LHS=RHS
Hence Proved
Step-by-step explanation:
Answered by
2
Step-by-step explanation:
(cosec A- sin A)(sec A-cos A)
L.H.S= (1/sin A-sin A)(1/cos A-cosA)
=(1-sin²A/sin A)(1-cos²A/cosA)
=(cos ²A/sinA)(sin²A/cos A)
=cosA.sinA
R.H.S= 1/tanA +cot A
=(1/sinA/cos A+cos A/sin A)
=(1/sin²A+cos²A/cosA.sinA)
=1/1/cosA.sinA
=1×cosA.sinA/1
=cosA.sinA
L.H.S=R.H.S proved
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