Advertisement Remove all ads

If `Sin Theta = A/B` Find Sec θ + Tan θ in Terms of a and B. - Mathematics

If `sin theta = a/b` find sec θ + tan θ in terms of a and b.

Advertisement Remove all ads

Solution

We know `sin theta = "𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒"/"ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒"`

Let x be the adjacent side

By applying Pythagoras theorem

𝐴𝐶2 = 𝐴𝐵2 + 𝐵𝐶2

b2 = a2 + x2

x2 = b2 − a2

`x = sqrt(b^2 - a^2)`

`sec theta = (AB)/(BC) = b/(sqrt(b^2 - a^2))`

`tan theta = (AB)/(BC) = a/(sqrt(b^2 - a^2))`

`sec theta + tan theta = b/(b^2 - a^2) + a/(sqrt(b^2 - a^2))`

`= (b + a)/(sqrt(b^2 - a^2)) = (b+ a)/sqrt((b + a)(b - a)) = (b + a)/sqrt(b + a) - 1/(sqrt(b - a)) = sqrt((b + a)/(b - a))`

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 10 Maths
Chapter 10 Trigonometric Ratios
Exercise 10.1 | Q 28 | Page 25
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×