Download App

Sine and Cosine Formulae and Their Applications — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSine and Cosine Formulae and Their Applications3 Marks
Question
$\frac{\text{b}\sec\text{B + c}\sec\text{C}}{\tan\text{B}+\tan\text{C}}=\frac{\text{c}\sec\text{C + a}\sec\text{A}}{\tan\text{C}+\tan\text{A}}=\frac{\text{a}\sec\text{A + b}\sec\text{B}}{\tan\text{A}+\tan\text{B}}.$
✓

Answer

$\frac{\text{b}\sec\text{B + c}\sec\text{C}}{\tan\text{B}+\tan\text{C}}=\frac{\text{c}\sec\text{C + a}\sec\text{A}}{\tan\text{C}+\tan\text{A}}=\frac{\text{a}\sec\text{A + b}\sec\text{B}}{\tan\text{A}+\tan\text{B}}$ $\frac{\text{b}\sec\text{B + c}\sec\text{C}}{\tan\text{B}+\tan\text{C}}$ $=\frac{\text{k}\sin\text{B}\sec\text{B + k}\sin\text{C}\sec\text{C}}{\tan\text{B}+\tan\text{C}}$ $=\frac{\text{k}\sin\text{B}\frac{1}{\cos\text{B}}+\text{k}\sin\text{C}\frac{1}{\cos\text{C}}}{\tan\text{B}+\tan\text{C}}$ $=\frac{\text{k}\tan\text{B + k}\tan\text{C}}{\tan\text{B}+\tan\text{C}}=\frac{\text{k}(\tan\text{B}+\tan\text{C})}{\tan\text{B}+\tan\text{C}}=\text{k}$ Similarly, $\frac{\text{c}\sec\text{C}+\text{a}+\sec\text{A}}{\tan\text{C}+\tan\text{A}}=\text{k}$ Similarly, $\frac{\text{a}\sec\text{A}+\text{b}+\sec\text{B}}{\tan\text{A}+\tan\text{B}}=\text{k}$ Hence, it is proved that $\frac{\text{b}\sec\text{B + c}\sec\text{C}}{\tan\text{B}+\tan\text{C}}=\frac{\text{c}\sec\text{C + a}\sec\text{A}}{\tan\text{C}+\tan\text{A}}=\frac{\text{a}\sec\text{A + b}\sec\text{B}}{\tan\text{A}+\tan\text{B}}=\text{k}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 3 marks)" from Sine and Cosine Formulae and Their Applications→Sine and Cosine Formulae and Their Applications — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Find k such that $\text{k}+9,\text{k}-6$ and 4 from three consecutive terms of a G.P.
→
Find the $4^{th}$ term in the expansion of $(x - 2y)^{12}$.
→
For any two sets A and B, prove that.
$\text{A}\cap\text{B}\subset\text{A}.$
→
Find the rational number having the following decimal expansions:$0.\overline{231}$
→
Prove that $:\frac{\text{cosec}(90^{\circ}+\text{x})+\cot(450^\circ+\text{x})}{\text{cosec}(90^\circ-\text{x})+\tan(180^\circ-\text{x})} +\frac{\tan\text{x}(180^\circ+\text{x})+\sec(180^\circ-\text{x})}{\tan(360^\circ+\text{x})-\sec(-\text{x})}=2$
→
In an A.P., if $p^{th}$ term is $\frac { 1 } { q }$ and $q^{th}​​​​​​​$​​​​​​​ term is $\frac { 1 } { p },$ prove that the sum of first pq terms is $\frac { 1 } { 2 } ( p q + 1 ),$ where $p \neq q.$
→
Find the two numbers whose A.M. is 25 and G.M. is 20.
→
A and B are events such that P(A) = 0.42, P(B) = 0.48 and P(A and B) = 0.16. Determine
(i) P (not A) (ii) P (not B) and (iii) P (A or B)
→
If the sum of three numbers in A.P. is 24 and their product is 440, find the numbers.
→
If $\text{f(x)}=\log_\text{e}(1-\text{x})$ and $\text{g(x)}=[\text{x}],$ then determine the following functions: (fg)(0)
→