please ans trignometry class 12th
Answers
proof:-Divide numerator and denominator by cos∅
on Dividing we will get
LHS={(sec∅-tan∅)}^1/2/{(sec∅+tan∅)}1/2
multiplying by sec∅-tam∅ in both we get
LHS={sec∅-tan∅)^2}1/2/(1)^1/2
LHS=sec∅-tan∅
the value of sec∅-tan∅, should always be positive because we had taken it out from square root by squaring it
and square of any no. is always positive...
the value of sec∅ is greater than tan∅ in ∅ between π/2 to -π/2 ,,
so,sec∅-tan∅ will be positive
but the value of tan∅ become greater in ii) and third quadrant i.e from ∅ between π/2 to 3π/2
sec∅-tan∅, become negative in this case,whic is not possible
so to make it positive we multiply it by negative sign
then the value will be -sec∅+tan∅
{hope it helps}
Given:
√(1-sinA)/(1+SinA)
Solution:
Take L.H.S
→√(1-sinA)/(1+SinA)
Rationalise the given equation,
→√[(1-SinA)/(1+sinA)]×[(1-sinA)/(1+sinA)
→√(1-sin²A)/(1-sin²A)
→√(1-sin²A)/cos²A
→(1-sinA)/cosA
→1/cosA - sinA/cosA
→secA-tanA
mul by (-1)
→-secA+tan