Question

If sec A = 1 then sin A + cos A +tan =

Answer 1

Answer:

$\sf{The \ value \ of \ sin \ A+cos \ A+tan \ A \ is \ 1.}$

Given:

• $\sf{sec \ A=1}$

To find:

• $\sf{The \ value \ of \ sin \ A+cos \ A+tan \ A.}$

Solution:

$\sf{\leadsto{sec A=1...given}}$

$\sf{sec^{2}\theta=1+tan^{2}\theta...trigonometric \ identity}$

$\sf{But, \ here \ sec \ A=1}$

$\sf{\therefore{tan^{2}A=1-1=0}}$

$\sf{\therefore{tan \ A=0...(1)}}$

$\sf{Also,}$

$\sf{\dfrac{1}{sec \ A}=cos \ A}$

$\sf{\therefore{cos \ A=\dfrac{1}{1}=1...(2)}}$

$\sf{sin^{2}\theta+cos^{2}\theta=1...trigonometric \ identity}$

$\sf{\therefore{sin^{2}A=1-1=0}}$

$\sf{\therefore{sin \ A=0...(3)}}$

$\sf{\leadsto{sin \ A+cos \ A+tan \ A}}$

$\sf{from \ (1), \ (2) \ and \ (3)}$

$\sf{\leadsto{0+1+0}}$

$\sf{\leadsto{1}}$

$\sf\purple{\tt{\therefore{The \ value \ of \ sin \ A+cos \ A+tan \ A \ is \ 1.}}}$