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`        Given(sinθ + cosθ) / sinθcosθ = 1/3.What is the value of sin⁴θ – cos⁴θ? `
2 months ago

```							actually sayan i m pretty sure u have typed the ques incorrectly. but i ll still tell u the method to even solve this.let sin theta= s and cos theta= cso sin⁴θ – cos⁴θ= (s^2 – c^2)(s^2 + c^2)= (s^2 – c^2)(1)= s^2 – c^2= (s – c)(s+c)......(*)now, let s+c= xsc= yand s – c= znow, we see that x^2= s^2 +  c^2 + 2sc= 1+2y......(1)also, given that x/y= 1/3or y= 3x.....(2)from (1) and (2) eliminating y, we havex^2= 1+6xor x^2 – 6x – 1= 0x= 3 ± sqrt 10, but we know that the range of s+c is from – sqrt 2 to sqrt 2.hence, x= 3 – sqrt 10now, x^2 + z^2= 2or z= ± sqrt (2 – x^2)from (*), we need to find the value of xz. since both x and z are known, we can obtain the final answer.kindly approve :)
```
2 months ago
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