Question

secA - tanA = m then value of

secA^4-tanA^4-2secA​

Answer 1

Step-by-step explanation:

If sec a - tan a = 4, then what is the value of cosec a?

sec a - tan a = 4 …(1). Let

sec a + tan a = m …(2)

Add (1) and (2)

2sec a = 4+m, or

sec a = (m/2) +2.

Subtract (1) from (2)

2tan a = m-4, or

tan a = (m/2) - 2

But 1 + tan^2 a = sec^2 a, or

1 + [(m/2) - 2]^2 = [(m/2) +2]^2, or

1 + 0.25m^2–2m+4 = 0.25m^2+2m+4, or

1 = 4m, or

m = 0.25

tan a = (m/2) - 2 = (0.25/2)-2 = -1.875

cot a = 1/(-1.875) = -0.533333

cosec a = [cosec^2 a]^0.5 = [1+cot^2 a]^2

= [ 1+(-0.533333)2]^0.5

= 1.28444444^0.5

cosec a = 1.1333333

Answer 2

Answer:

ur answer

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Step-by-step explanation:

L.H.S

(1+tanA−secA)×(1+tanA+secA)

=(1+tanA)

2

−(secA)

2

[∵(a+b)(a−b)=a

2

−b

2

)]

=1+tan

2

A+2tanA−sec

2

A

=sec

2

A+2tanA−sec

2

A [∵sec

2

θ=1+tan

2

θ]

=2tanA

=R.H.S.

∴L.H.S=R.H.S

(1+tanA−secA)×(1+tanA+secA)=2tanA

Hence proved.