please answer this question
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dhanushmarch:
pls answer
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Answered by
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Answer:
Step-by-step explanation:
Here, let theta be taken as x.
LHS
(1+tanx+secx) (1+cotx-cosecx)
= (1+sinx/cosx+1/cosx) (1+cosx/sinx-1/sinx)
= (cosx+sinx+1/cosx) (sinx+cosx-1/sinx)
= {(sinx+cosx)+1/cosx} {(sinx+cosx)-1/sinx}
= {(sinx+cosx)²-(1)²} / {sinxcosx}
= {(sin²x+cos²x+2sinxcosx)-1} / {sinxcosx}
= 1+2sinxcosx-1) / sinxcosx [sin²x+cos²x = 1]
= 2sinxcosx /sinxcosx
= 2 = RHS [Proved}
Answered by
1
Here, let theta be taken as x.
LHS
(1+tanx+secx) (1+cotx-cosecx)
= (1+sinx/cosx+1/cosx) (1+cosx/sinx-1/sinx)
= (cosx+sinx+1/cosx) (sinx+cosx-1/sinx)
= {(sinx+cosx)+1/cosx} {(sinx+cosx)-1/sinx}
= {(sinx+cosx)²-(1)²} / {sinxcosx}
= {(sin²x+cos²x+2sinxcosx)-1} / {sinxcosx}
= 1+2sinxcosx-1) / sinxcosx [sin²x+cos²x = 1]
= 2sinxcosx /sinxcosx
= 2 = RHS [Proved}
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