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# Verify Trigonometric Identity (1+sec x)/(tan x + sin x)=csc x?

### 3 Answers

- 1 decade agoFavorite Answer
(1+ secx) / (tanx + sinx) = cscx {multiply (tanX + Sinx by both sides to get out of the denominator}

(1 + Secx) = Csc(TanX + SinX) {you will need to distribute, and break down Csc}

(1 + SecX) = (1 / SinX)(SinX / CosX) + (1/SinX)(SinX) {multiply out}

1 + SecX = (Sinx / [(SinX)(CosX)]) + (SinX / SinX)

1 + SecX = (1 / CosX) + 1

1 + SecX = 1 + (1 / CosX)

1 + (1 / CosX) = 1 + (1 / CosX)

Checks!

- 1 decade ago
1+sec(x) = 1 + [1/cos(x)]

=[cos(x)+1]/cos(x)

tan x + sin x = (sinx/cosx)+sinx

=[sinx + sinx.cosx] / cosx

=sinx[cosx+1] / cosx

[1+sec(x)] / [tan x + sin x]=1 / sinx

=csc x

- ComoLv 71 decade ago
LHS

----------

1 + sec x

------------------

tan x + sin x

cos x + 1

----------------------------

sin x + cos x sin x

cos x + 1

--------------------------

sin x ( 1 + cos x )

1

--------

sin x

csc x

RHS

--------

csc x

LHS = RHS