Math, asked by krithi2001143, 1 year ago

Ριεαsε sοινε:
(1 + cotθ - cosecθ)(1 + tanθ + secθ) = 2
βεsτ αηsωεr ωiιι βε sειεςτεδ αs τhε βrαiηιiεsτ αηsωεr...


vardhmansurana1008: ncrt question
JaydattaPatwwe: R u in 10th std

Answers

Answered by noor0
6
hey mate,,,,,

here is the solution of your question
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all you need to do is expand it. 

1 + tanθ + secθ+ cotθ + tanθcotθ + secθcotθ - cscθ - cscθtanθ - cscθsecθ 

1 + sinθ/cosθ + 1/cosθ + cosθ/sinθ + tanθ * 1/tanθ + 1/sinθ - 1/sinθ - sinθ/cosθ - 1/sinθ * 1/cosθ 

1 + 1/sinθcosθ + 1/cosθ + 1 - 1/cosθ - 1/sinθcosθ 

2

I hope it will help you,,,,,,,,
Answered by JaydattaPatwwe
3

(1 + cotθ - cosecθ)(1 + tanθ + secθ)=2

LHS= ( 1 + cosθ/sinθ - 1/sinθ)(1 +sinθ/cosθ + 1/cosθ) -------------------

[cotx = cosx/sinx, cosecx =1/sinx, tanx=sinx/cosx, secx =cosx]

=({sinθ + cosθ -1}/sinθ)({cosθ +sinθ +1}/cosθ)

=[{(sinθ + cosθ) - 1}{(sinθ + cosθ) + 1}]/sinθcosθ

=[(sinθ + cosθ)² - 1]/sinθcosθ--------------[(a - b)(a+b)= a² +b²]

=[sin²θ + cos²θ + 2sinθcos - 1]/sinθcosθ-----------------{sin²x + cos²x =1]

= 2sinθcosθ/sinθcosθ = 2

=RHS

Hence proved.

Hope it helps.

Cheers!


JaydattaPatwwe: Pls mark as brainliest if it helps
JaydattaPatwwe: Ask if you have any doubts
JaydattaPatwwe: Hey this question is in 10th std NCERT right??
JaydattaPatwwe: Nothing I still remember the question it came in our Final exams when we were in 10th.(basically last year)
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