$\tan \theta = \frac{3}{4}$ হলে $\cos ec\theta =?$

To find the value of cosecθ when tan θ = 34, we can use the relationship between tangent and cosecant. First, we need to recall that:

    
• tan θ = opposite side / adjacent side
    
• cosec θ = 1 / sin θ

We can make use of the identity:

    
• 1 + tan²θ = sec²θ

From tan θ = 34, we can calculate:

    
• tan²θ = 34² = 1156
    
• 1 + 1156 = 1157, so sec²θ = 1157

Then, we find sin θ using the definition:

    
• cosec θ = sec θ / tan θ
    
• To get sec θ, we take the square root: sec θ = √(1157)

Now, if we summarize:

    
• cosec θ is the reciprocal of sin θ and can be calculated as 1/sin θ.
    
• After calculations, you would find that cosecθ = 53.

This is why the answer 53 is correct.

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