If c o s α + β = 3 5   , sin ⁡ ( α - β ) = 5 13 and 0 < α , β < π 4 , then tan ⁡ 2 α is equal to:

Question

If c o s &#945; + &#946; = 3 5 &#160; , sin &#8289; ( &#945; - &#946; ) = 5 13 and 0 &#60; &#945; , &#946; &#60; &#960; 4 , then tan &#8289; 2 &#945; is equal to:

Aicharya · Accepted Answer

c o s &#945; + &#946; = 3 5 &#8658; t a n &#945; + &#946; = 4 3 s i n ( &#945; - &#946; ) = 5 13 &#8658; t a n ( &#945; - &#946; ) = 5 12 Now, t a n 2 &#945; = t a n &#945; + &#946; + &#945; - &#946; = t a n ( &#945; + &#946; ) + t a n ( &#945; - &#946; ) 1 - t a n ( &#945; + &#946; ) t a n ( &#945; - &#946; ) = 4 3 + 5 12 1 - 4 3 &#215; 5 12 = 63 16

If c o s α + β = 3 5   , sin ⁡ ( α - β ) = 5 13 and 0 < α , β…

Solution

If c o s &#945; + &#946; = 3 5 &#160; , sin &#8289; ( &#945; - &#946; ) = 5 13 and 0 &#60; &#945; , &#946;…

Solution

If c o s α + β = 3 5 , sin ⁡ ( α - β ) = 5 13 and 0 < α , β…