If cot α = 1 and sec β = - 5 3 , where π < α < 3 π 2 and π 2 < β < π , then the value of tan α + β and the quadrant in which α + β lies, respectively are

Question

If cot &#945; = 1 and sec &#946; = - 5 3 , where &#960; &#60; &#945; &#60; 3 &#960; 2 and &#960; 2 &#60; &#946; &#60; &#960; , then the value of tan &#945; + &#946; and the quadrant in which &#945; + &#946; lies, respectively are

Aicharya · Accepted Answer

Given, cot &#945; = 1 , sec &#946; = - 5 3 So, cos &#946; = - 3 5 , tan &#946; = - 4 3 and tan &#945; = 1 Now using formula tan &#945; + &#946; = tan &#945; + tan &#946; 1 - tan &#945; tan &#946; &#8658; tan &#945; + &#946; = 1 - 4 3 1 + 4 3 &#215; 1 = - 1 7 We know that tan &#952; is negative in 2 n d &#160; &#38; &#160; 4 t h quadrant but as &#960; &#60; &#945; &#60; 3 &#960; 2 , so &#945; + &#946; will lie in IV th quadrant.

If cot α = 1 and sec β = - 5 3 , where π < α < 3 π 2 and π 2 <…

Solution

If cot &#945; = 1 and sec &#946; = - 5 3 , where &#960; &#60; &#945; &#60; 3 &#960; 2 and &#960; 2 &#60;…

Solution

If cot α = 1 and sec β = - 5 3 , where π < α < 3 π 2 and π 2 <…