Integrate the function $\frac{\tan\left(x\right)}{\sin\left(x\right)^2\sec\left(x\right)+\cos\left(x\right)}$ from $\frac{\pi }{2}$ to $\pi $

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$\int_{\frac{\pi}{2}}^{\pi }\frac{\tan\left(x\right)}{\sin\left(x\right)^2\sec\left(x\right)+\cos\left(x\right)}dx$

Learn how to solve definite integrals problems step by step online. Integrate the function tan(x)/(sin(x)^2sec(x)+cos(x)) from pi/2 to pi. Simplifying. Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Divide fractions \frac{\frac{\sin\left(x\right)}{\cos\left(x\right)}}{\sin\left(x\right)^2\sec\left(x\right)+\cos\left(x\right)} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}. Multiply the single term \cos\left(x\right) by each term of the polynomial \left(\sin\left(x\right)^2\sec\left(x\right)+\cos\left(x\right)\right).