0

Guest

Courses New

(1+sint ) ( 1 + cost ) = 5 / 4 Find the value of ( 1 - sint ) ( 1 - cost ).

(1+sint ) ( 1 + cost ) = 5 / 4 Find the value of ( 1 - sint ) ( 1 - cost ).

Grade:12

2 Answers

mycroft holmes
272 Points
8 years ago
My solution disappeared!! Hint: sin t cos t = ½ [(sin t + cost)2-1]. So use substitution sin t +cos t = y, and solve for y. Required expression is 5/4 – 2y
Ajaiy Prabhu
34 Points
8 years ago
 $2\sin t \cos t + 2 \sin t + 2 \cos t = \frac{1}{2}$, and adding $\sin^2 t + \cos^2t = 1$
$(\sin t + \cos t)^2 + 2(\sin t + \cos t) = \frac{3}{2}$.
Completing the square on the left in the variable $(\sin t + \cos t)$ gives
 $\sin t + \cos t = -1 \pm \sqrt{\frac{5}{2}}$
$\sin t + \cos t = \sqrt{\frac{5}{2}} - 1$
Subtracting twice this from our original equation
$(\sin t - 1)(\cos t - 1) = \sin t \cos t - \sin t - \cos t + 1 = \frac{13}{4} - \sqrt{10}$
 

Think You Can Provide A Better Answer ?

Other Related Questions on Trigonometry

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More