sec(x) - cosec(x) = 4/3 then what is sin(x) -cos(x)
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As we know,
Sec(x) =
Cosec(x) =
Hence, we will convert given equation in form of cos(x) and sin(x)
sec(x) - cosec(x) = 4/3
=>
-
= 4/3
=>
Multiplying denominator both sides by -2,
=>[tex] \frac{sin(x) - cos(x)}{-2cos(x).sin(x)} = \frac{4}{3(-2)} [/tex]
Adding and subtracting 1 from left side denominator,

=>
=>
Let us assume (sin(x)-cos(x) = p
=>
=>
=>
=>(2p+1)(p+2) = 0
=> p = -
, -2
sin(x) - cos(x) can never be -2 (if sin(x) = -1, cos(x)
1)
Hence, sin(x)-cos(x) = -
Sec(x) =
Cosec(x) =
Hence, we will convert given equation in form of cos(x) and sin(x)
sec(x) - cosec(x) = 4/3
=>
=>
Multiplying denominator both sides by -2,
=>[tex] \frac{sin(x) - cos(x)}{-2cos(x).sin(x)} = \frac{4}{3(-2)} [/tex]
Adding and subtracting 1 from left side denominator,
=>
=>
Let us assume (sin(x)-cos(x) = p
=>
=>
=>
=>(2p+1)(p+2) = 0
=> p = -
sin(x) - cos(x) can never be -2 (if sin(x) = -1, cos(x)
Hence, sin(x)-cos(x) = -
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