Step-by-step Solution

Prove the trigonometric identity $\sec\left(x\right)=\frac{\cos\left(x\right)}{2\left(1+\sin\left(x\right)\right)}+\frac{\cos\left(x\right)}{2\left(1-\sin\left(x\right)\right)}$

Go!
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Step-by-step explanation

Problem to solve:

$sec\:x\:=\frac{cos\:x}{2\left(1+\:sen\:x\right)}+\frac{cos\:x}{2\left(1-\:sen\:x\right)}$

Learn how to solve trigonometric identities problems step by step online.

$\sec\left(x\right)=\frac{2\cos\left(x\right)\left(1-\sin\left(x\right)\right)+2\cos\left(x\right)\left(1+\sin\left(x\right)\right)}{4\left(1+\sin\left(x\right)\right)\left(1-\sin\left(x\right)\right)}$

Unlock this full step-by-step solution!

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity sec(x)=(cos(x)/(2(1+sin(x)))+(cos(x)/(2(1-sin(x))). Combine fractions with different denominator using the formula: \displaystyle\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d + b\cdot c}{b\cdot d}. Solve the product of difference of squares 4\left(1+\sin\left(x\right)\right)\left(1-\sin\left(x\right)\right). Apply the identity: 1-\sin\left(x\right)^2=\cos\left(x\right)^2. Solve the product 2\cos\left(x\right)\left(1-\sin\left(x\right)\right).

Final Answer

true
$sec\:x\:=\frac{cos\:x}{2\left(1+\:sen\:x\right)}+\frac{cos\:x}{2\left(1-\:sen\:x\right)}$

Steps:

10

Time to solve it:

~ 0.18 s (SnapXam)