Question

prove that 1/sec x-tan x -1/cos x =1/cos x - 1/sec x +tan x​

Answer 1

Step-by-step explanation:

We have secx+tanx=k...........1

From 2nd identity

sec

2

x−tan

2

x=1

a

2

−b

2

=(a+b)(a−b)

(secx+tanx)(secx−tanx)=1

(k)(secx−tanx)=1 from eq 1

secx−tanx=

k

1

............2

adding equations 1 and 2, then we get

secx+tanx+secx−tanx=1+

k

1

secx+secx=1+

k

1

2secx=k

2

+

k

1

secx=k

2

+

2k

1

we know that secx=

cosx

1

cosx=

k

1

2

+

2k

1

cosx=

k

2

+1

2k

we know that from 1st identity

sinx=

(1−cosx

2

)

sinx=

(1−(

(k

2

+1)

2

2k

)

sinx=

(k

2

+1)

2

(1−4k

2

)

sinx=

k

2

+1

(k

2

+1)

2

−4k

2

sinx=

(k

2

+1)

2

(k

2

−1)

2

sinx=

k

2

+1

k

2

−1

Hence proved

Answer 2

Answer:

The given statement is proved