ϙ. ɪғ sᴇᴄ ᴛʜᴇᴛᴀ ɪs ᴇϙᴜᴀʟ ᴛᴏ X + 1/ 4x ᴀɴᴅ x ɪs ɴᴏᴛ ᴇϙᴜᴀʟ ᴛᴏ ᴢᴇʀᴏ ᴛʜᴇɴ ғɪɴᴅ (sᴇᴄ ᴛʜᴇᴛᴀ + ᴛᴀɴ ᴛʜᴇᴛᴀ)
Answers
Question:
If sec theta is equal to X+1/4× and x is not equal to zero then find (Sex theta + tan theta)
Answer:
Given –
secA = x + 1/4x
As 1 + tan^2A = sec^2A
tan^2A = sec^2A – 1
Therfore, tan^2A = (x + 1/4x)^2 – 1
= x^2 + 2*x*1/4x + 1/16x^2 – 1
= x^2 + 1/2 + 1/16x2 – 1
= x^2 + 1/16x^2 – 1/2
= (x – 1/4x)^2
Therefore, tan^2A = x – 1/4x or tan^2A = - (x – 1/4x)
Substitute the value of secA and tanA in the given equation secA + tanA
LHS = secA + tanA
= x + 1/4x + x – 1/4x
= 2x
= RHS
Or
LHS = secA + tanA
=x + 1/4x -x + 1/4x
= 2/4x
= 1/2x
= RHS
Hence proved.
Hope it helps you