1/secx-tanx- 1/cosx= 1cosx-1/secx+tanx
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Answer:
Step-by-step explanation:
L.H.S:
//multiply the numerator and denominator of 1/secx-tanx with (secx+tanx)
secx+tanx/(secx-tanx)(secx+tanx) - 1/cosx
= secx+tanx/sec²x - tan²x - secx
//remember sec²x - tan²x = 1
= secx + tanx - secx = tanx.
R.H.S:
//multiply the numerator and denominator of 1/secx+tanx with (secx-tanx)
= 1/cosx - (secx -tanx)/(secx+tanx)(secx-tanx)
= 1/cosx - (secx -tanx) / sec²x - tan²x
//remember sec²x - tan²x = 1
= 1/cosx - (secx-tanx)
= secx - secx + tanx
= tanx.
L.H.S =R.H.S
Hence proved.
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