Question
Evaluate the following:
$\frac{5\cos^260^\circ+4\sec^230^\circ-\tan^245^\circ}{\sin^230^\circ+\cos^230^\circ}$
$\frac{5\cos^260^\circ+4\sec^230^\circ-\tan^245^\circ}{\sin^230^\circ+\cos^230^\circ}$
✓
Answer
$\frac{5\cos^260^\circ+4\sec^230^\circ-\tan^245^\circ}{\sin^230^\circ+\cos^230^\circ}$
$=\frac{5\big(\frac12\big)^2+4\big(\frac{2}{\sqrt{3}}\big)^2-(1)^2}{\big(\frac12\big)^2+\Big(\frac{\sqrt{3}}{2}\Big)^2}$
$=\frac{\Big(\frac54+\frac{4+4}{3}-1\Big)}{\Big(\frac14+\frac34\Big)}$
$=\frac{\Big(\frac{5}{4}+\frac{16}{3}-\frac{1}{1}\Big)}{\big(\frac44\big)}$
$=\frac{\big(\frac{15+64-12}{12}\big)}{\big(\frac44\big)}$
$=\frac{\big(\frac{67}{12}\big)}{(1)}$
$=\frac{67}{12}$
$=\frac{5\big(\frac12\big)^2+4\big(\frac{2}{\sqrt{3}}\big)^2-(1)^2}{\big(\frac12\big)^2+\Big(\frac{\sqrt{3}}{2}\Big)^2}$
$=\frac{\Big(\frac54+\frac{4+4}{3}-1\Big)}{\Big(\frac14+\frac34\Big)}$
$=\frac{\Big(\frac{5}{4}+\frac{16}{3}-\frac{1}{1}\Big)}{\big(\frac44\big)}$
$=\frac{\big(\frac{15+64-12}{12}\big)}{\big(\frac44\big)}$
$=\frac{\big(\frac{67}{12}\big)}{(1)}$
$=\frac{67}{12}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find the area of the largest triangle that can be inscribed in a semi-circle of radius r units.
A jar contains 54 marbles, each of which some are blue, some are green and some are white. The probabiliy of selecting a blue marble at random is $\frac{1}{3}$ and the probability of selecting a green marble at random is $\frac{4}{9}.$ How many white marbles does the jar contain?
→Very-Short and Short-Answer Qustions:
If $\cos\text{B}=\frac35$ and $(\text{A}+\text{B})=90^\circ,$ what is the value of $\sin\text{A}.$
→If $\cos\text{B}=\frac35$ and $(\text{A}+\text{B})=90^\circ,$ what is the value of $\sin\text{A}.$
In Δ ABC, seg BD bisects ∠ ABC. If AB = x, BC = x + 5, AD = x – 2, DC = x + 2, then find the value of x.
Find the $n^{th}$ term of the following APs:
$5, 11, 17, 23,....$
→$5, 11, 17, 23,....$
Solve the following simultaneous equation.
5x + 2y = –3; x + 5y = 4
5x + 2y = –3; x + 5y = 4
The points $A\left(x_1, y_1\right), B\left(x_2, y_2\right)$ and $C\left(x_3, y_3\right)$ are the vertices of $\triangle A B C$.
Find the coordinates of the point $P$ on $A D$ such that $A P: P D=2: 1$.
→Find the coordinates of the point $P$ on $A D$ such that $A P: P D=2: 1$.
The Sum and product of the zeros of a quadratic polynomial are $-\frac{1}{2}$ and $-3$ respectively. What is the quadratic polynomial?
→Prove that $\sec^2\theta + cosec^2\theta = \sec^2\theta \times cosec^2\theta $
→A bag contains 50 cards. Each card bears only one number from 1 to 50. One
card is drawn at randomfrom the bag. Write the sample space. Also write the
events A, B and find the number of sample points in them.
(i) Condition for event A : the number on the card is divisible by 6.
(ii) Condition for event B : the number on the card is a complete square.
card is drawn at randomfrom the bag. Write the sample space. Also write the
events A, B and find the number of sample points in them.
(i) Condition for event A : the number on the card is divisible by 6.
(ii) Condition for event B : the number on the card is a complete square.