AP EAMCET · Maths · Trigonometric Ratios & Identities

If $\sec \theta=m, \tan \theta=n$, then $\frac{1}{m}\left[m+n+\frac{1}{m+n}\right]=$

A 1
B 2
C -1
D 3

Verified Solution

Answer & Solution

Correct Answer

(B) 2

Step-by-step Solution

Detailed explanation

Given, $\sec \theta=m, \tan \theta=n$…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

The value of $\tan (\frac{7 π}{8})$ is

AP EAMCET 2022 Easy
A point $P(x, y)$ is such that the sum of squares of its distance from $(a, 0)$ and $(-a, 0)$ is $2 b^2$. The equation representing the locus of $P$ is

AP EAMCET 2022 Easy
If the point $(a, 8, - 2)$ divides the line segment joining the points $(1, 4, 6)$ and $(5, 2, 10)$ in the ratio $m : n$ then $\frac{2 m}{n} - \frac{a}{3} =$

AP EAMCET 2022 Easy
If $\cosh x=\operatorname{cosec} \theta$, then $\operatorname{coth} 2 \frac{x}{2}=$

AP EAMCET 2023 Hard
A bag contains $n$ white and $n$ black balls. Pairs of balls are drawn at random without replacement successively, until the bag is empty. If the number of ways in which each pair consists of one white and one black ball is 14400 , then $n$ is equal to

AP EAMCET 2011 Medium
A manufacturing company noticed that $1 \%$ of its products are defective. If a dealer orders for 300 items from this company, then the probability that the number of defective items is atmost one is

AP EAMCET 2024 Medium

Explore more questions on app

From AP EAMCET

If $f(x)=\int \operatorname{cosec}^5 x d x$, then $f\left(\frac{\pi}{4}\right)=$

AP EAMCET 2018 Medium
If $P$ and the origin are the points of intersection of the parabolas $y^2=32 x$ and $2 x^2=27 y$; and if $\theta$ is the acute angle between these curves at $P$, then $5 \sqrt{\tan \theta}=$

AP EAMCET 2018 Medium
The number of 5-digited number which are not divisible by 5 and which consists of different odd digits is

AP EAMCET 2002 Medium
In a city, 10 accidents take place in a span of 50 days.Assuming that the number of accidents follow the Poisson distribution,the probability that three or more accidents occur in a day, is

AP EAMCET 2016 Hard
The mean of numbers $a, b, 8,5,10$ is 6 and their variance is 6.80. Then $\operatorname{Tan}^{-1} \frac{1}{a}+\operatorname{Tan}^{-1} \frac{1}{b}=$

AP EAMCET 2017 Easy
If $\alpha, \beta, \gamma$ are the roots of the equation $\mathrm{x}^3+\mathrm{px}^2+\mathrm{qx}+\mathrm{r}=0$, then $(\alpha+\beta)(\beta+\gamma)(\gamma+\alpha)=$

AP EAMCET 2025 Medium

Explore more questions on app

If \(\sec \theta=m, \tan \theta=n\), then \(\frac{1}{m}\left[m+n+\frac{1}{m+n}\right]=\)

Answer & Solution

Step-by-step Solution

See the Complete Solution