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Solve for x in the following equations.

0 votes
((1+sinx)/cosx)+(cosx/((1+sinx))
asked Jun 24, 2013 in TRIGONOMETRY by dkinz Apprentice

2 Answers

0 votes

The given equation is =image

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Apply pythagoreen identity :image

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Cancel common terms.

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answered Jun 24, 2013 by tom Novice
0 votes

Given equation is( (1 +sinx)/cosx) + (cosx/(1+sinx)

Take L.C.M  ((1+sinx)^2 + (cosx)^2)/cosx(1+sinx)

It is in the form of (a+b)^2 = a^2 + b^2 + 2ab

(1 + sinx + 2sinx+cosx^2)/cosx(1+sinx)

We have formula sin^2x + cos^2x =1

(1 + 1 +2sinx)/(cosx +cosxsinx)

(2 +2sinx)/cosx(1+sinx)

Take common factor 2 in numerator

2(1 + sinx)/cosx(1 + sinx)

Cancel (1 + sinx) in numerator and denominator

2/cosx = 2secx

The solution for x = arccos(2)

answered Jun 25, 2013 by jouis Apprentice

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