If sec θ = x + 1/4x, x ≠ 0, then how can (sec θ – tan θ) be expressed as?
Rishabh Sankla , 5 Years ago
Grade 11
Trigonometry> If sec θ = x + 1/4x , x ≠ 0 , then how ca...
1 Answers
Arun
Last Activity: 5 Years ago
Given:
secϴ = x + 1/4x…….(1)
tan²ϴ = sec²ϴ -1
tan²ϴ = (x + 1/4x)² -1
[From equation 1]
tan²ϴ = x² + 1/16x² +½ -1
[ (a+b)² = a² + 2ab +b²]
tan²ϴ = x² + 1/16x² - ½
tan²ϴ = (x - 1/4x)²
[a² +b²-2ab = (a-b)²]
tanϴ = ±(x - 1/4x)
[Taking square roots both sides]
tanϴ = (x - 1/4x) or - (x - 1/4x)
When tanϴ = (x - 1/4x), then
secϴ +tanϴ = x +1/4x + x -1/4x = 2x
[From equation 1]
secϴ +tanϴ = 2x
When tanϴ = - (x - 1/4x), then
secϴ +tanϴ = (x +1/4x) -( x -1/4x )
[From equation 1]
= x +1/4x - x + 1/4x
= 1/4x + 1/4x = 2/4x = 1/2x
Hence secϴ - tanϴ = 2x
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