S L Loney Solutions for Chapter: Trigonometrical Ratios for Angles Less than a Right Angle, Exercise 2: EXAMPLES VI

If $8\sin \text{θ}=4+\cos \text{θ},$ find $\sin \text{θ}$, where $\text{θ}$ is an acute angle.

If $\tan \text{θ}+\sec \text{θ}=1.5$, find $\sin \text{θ}$ where $\text{θ}$ is an acute angle

If $\mathrm{cot\theta }+\mathrm{cosec\theta }=5,$ find $\cos \text{θ}$ where $\text{θ}$ is an acute angle

If $3{\sec }^4\text{θ}+8=10{\sec }^2\text{θ}$, find the values of $\tan \text{θ}$ where $\text{θ}$ is an acute angle

If ${\tan }^2\theta +\sec \theta =5,$ find $\cos \theta$ where $\theta$, is an acute angle.

If $\tan \text{θ}+\cot \text{θ}=2$, then find $\sin \text{θ}$, where $\text{θ}$ is less than a right angle.

If ${\sec }^2\text{θ}=2+2\tan \text{θ}$, find $\tan \text{θ}$, where $\text{θ}$ is less than a right angle.

If $\tan \theta =\frac{2x\left(x+1\right)}{2x+1}$, find $\sin \theta$ and $\cos \theta$, for the acute angle $\theta$.